Project-Team CARDAMOM · Project-Team CARDAMOM Certiﬁed Adaptive discRete moDels for robust...

IN PARTNERSHIP WITH:Institut Polytechnique deBordeaux

Université de Bordeaux

Activity Report 2016

Project-Team CARDAMOM

Certified Adaptive discRete moDels for robustsimulAtions of CoMplex flOws with Movingfronts

IN COLLABORATION WITH: Institut de Mathématiques de Bordeaux (IMB)

RESEARCH CENTERBordeaux - Sud-Ouest

THEMENumerical schemes and simulations

Table of contents

1. Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Overall Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1. Overall Objectives 22.2. Scientific context and challenges 22.3. Our approach 3

3. Research Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.1. Variational discrete asymptotic modelling 43.2. High order discretizations on moving adaptive meshes 53.3. Coupled approximation/adaptation in parameter and physical space 73.4. Robust multi-fidelity modelling for optimization and certification 8

4. Application Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84.1. De-anti icing systems 84.2. Space re-entry 94.3. Energy 114.4. Materials engineering 134.5. Coastal and civil engineering 13

5. New Software and Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.1. AeroSol 145.2. CAKE 175.3. Crysa 175.4. Cut-ANOVA 175.5. Fmg 185.6. MMG3D 185.7. Mmg platform 195.8. NOMESH 195.9. SLOWS 205.10. Sparse-PDD 205.11. TUCWave 21

6. New Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.1. High order discretizations on unstructured meshes 216.2. High order mesh generation and mesh adaptation 226.3. Uncertainty Quantification and robust design optimization 226.4. Modelling of free surface flows 246.5. Wave energy conversion hydrodynamics 25

7. Bilateral Contracts and Grants with Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258. Partnerships and Cooperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

8.1. Regional Initiatives 268.2. National Initiatives 26

8.2.1. ANR MAIDESC 268.2.2. PIA TANDEM 278.2.3. APP Bordeaux 1 278.2.4. APP University of Bordeaux 27

8.3. European Initiatives 288.3.1. FP7 & H2020 Projects 28

8.3.1.1. UTOPIA 288.3.1.2. STORM 28

8.3.2. Collaborations in European Programs, Except FP7 & H2020 298.4. International Initiatives 29

8.4.1.1. AQUARIUS2 29

2 Activity Report INRIA 2016

8.4.1.2. AMoSS 308.4.1.3. Informal International Partners 30

8.5. International Research Visitors 319. Dissemination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.1. Promoting Scientific Activities 319.1.1. Scientific Events Organisation 319.1.2. Scientific Events Selection 329.1.3. Journal 32

9.1.3.1. Member of the Editorial Boards 329.1.3.2. Reviewer - Reviewing Activities 32

9.1.4. Invited Talks 329.1.5. Leadership within the Scientific Community 32

9.2. Teaching - Supervision - Juries 339.2.1. Teaching 339.2.2. Supervision 339.2.3. Juries 34

10. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

Project-Team CARDAMOM

Creation of the Team: 2015 January 01, updated into Project-Team: 2016 June 01

Keywords:

Computer Science and Digital Science:6.1.1. - Continuous Modeling (PDE, ODE)6.1.4. - Multiscale modeling6.1.5. - Multiphysics modeling6.2.1. - Numerical analysis of PDE and ODE6.2.6. - Optimization6.2.8. - Computational geometry and meshes6.3.1. - Inverse problems6.3.4. - Model reduction6.3.5. - Uncertainty Quantification

Other Research Topics and Application Domains:3.3.2. - Water: sea & ocean, lake & river3.3.3. - Littoral3.4.1. - Natural risks4.3.2. - Hydro-energy5.2.1. - Road vehicles5.2.3. - Aviation5.2.4. - Aerospace5.5. - Materials

1. MembersResearch Scientists

Pietro Marco Congedo [Inria, Researcher, HDR]Maria Kazolea [Inria, Researcher]Mario Ricchiuto [Team leader, Inria, Senior Researcher, HDR]

Faculty MembersHéloise Beaugendre [Bordeaux INP, Associate Professor, HDR]Mathieu Colin [Bordeaux INP, Associate Professor, HDR]Cecile Dobrzynski [Bordeaux INP, Associate Professor]Luc Mieussens [Bordeaux INP, Professor]

EngineersAlgiane Froehly [Univ. Bordeaux]Nikolaos Pattakos [Inria (SED)]Jean Mercat [Inria]

PhD StudentsLuca Arpaia [Inria]Stevan Bellec [Univ. Bordeaux]Umberto Bosi [Inria]Andrea Cortesi [Inria]

https://raweb.inria.fr/rapportsactivite/RA2016/static/keywords/ComputerScienceandDigitalScience.html

https://raweb.inria.fr/rapportsactivite/RA2016/static/keywords/OtherResearchTopicsandApplicationDomains.html


Aurore Fallourd [Univ. Bordeaux, from Oct 2016]Andrea Filippini [Inria]Xi Lin [Univ. Bordeaux]Leo Nouveau [Inria]Simon Peluchon [CEA]Nassim Auguste Razaaly Jamal [Inria]Barbara Re [Politecnico di Milano, until Sep 2016]Mickael Rivier [Inria]François Sanson [Inria]Quentin Viville [Univ. Bordeaux]

Post-Doctoral FellowsSebastien de Brye [Univ. Bordeaux]Ghina El Jannoun [Inria, until Feb 2016]Marco Lorini [Inria, from Nov 2016]Giorgio Martalo [Univ. Bordeaux]

Administrative AssistantsAnne-Laure Gautier [Inria]Nicolas Jahier [Inria]

2. Overall Objectives

2.1. Overall ObjectivesCARDAMOM is a joint team of Inria Bordeaux - Sud-Ouest, University of Bordeaux and Bordeaux Inst. Nat. Poly-technique) and IMB (Institut de Mathématiques de Bordeaux – CNRS UMR 5251, University of Bordeaux).CARDAMOM has been created on January 1st, 2015 (https://team.inria.fr/cardamom/). The CARDAMOM projectaims at providing a robust modelling strategy for engineering applications involving complex flows with mov-ing fronts. The term front here denotes either an actual material boundary (e.g. multiple phases), a physicaldiscontinuity (e.g. shock waves), or a transition layer between regions with completely different dominantflow behaviour (e.g. breaking waves). These fronts introduce a multi-scale behaviour. The resolution of all thescales is however not feasible in certification and optimization cycles, and not necessary in many engineeringapplications, while in others it is enough to model the average effect of small scales on large ones (closuremodels). We plan to develop application-tailored models obtained by a tight combination of asymptotic PDE(Partial Differential Equations) modelling, adaptive high order PDE discretizations, and a quantitative certifi-cation step assessing the sensitivity of outputs to both model components (equations, numerical methods, etc)and random variations of the data. The goal is to improve parametric analysis and design cycles, by increas-ing both accuracy and confidence in the results thanks to improved physical and numerical modelling, and toa quantitative assessment of output uncertainties. This requires a research program mixing of PDE analysis,high order discretizations, Uncertainty Quantification (UQ), robust optimization, and some specific engineer-ing know how. Part of these scientific activities started in the BACCHUS and MC2 teams. CARDAMOM harmonizesand gives new directions to this know how.

2.2. Scientific context and challengesThe objective of this project is to provide improved analysis and design tools for engineering applicationsinvolving fluid flows, and in particular flows with moving fronts. In our applications a front is either anactual material interface, or a well identified and delimited transition region in which the flow undergoes achange in its dominant macroscopic character. One example is the certification of wing de anti-icing systems,involving the predictions of ice formation and detachment, and of ice debris trajectories to evaluate the riskof downstream impact on aircraft components [131], [67]. Another application, relevant for space reentry, isthe study of transitional regimes in high altitude gas dynamics in which extremely thin layers appear in the

https://team.inria.fr/cardamom/

Project-Team CARDAMOM 3

flow which cannot be analysed with classical continuous models (Navier-Stokes equations) used by engineers[73], [98]. An important example in coastal engineering is the transition between propagating and breakingwaves, characterized by a strong local production of vorticity and by dissipative effects absent when wavespropagates [75]. Similar examples in energy and material engineering provide the motivation of this project.

All these application fields involve either the study of new technologies (e.g. new design/certification tools foraeronautics [81], [93], [111], [67] or for wave energy conversion [91]), or parametric studies of complexenvironments (e.g. harbour dynamics [100], or estuarine hydrodynamics [62]), or hazard assessment andprevention [95]. In all cases, computationally affordable, quick, and accurate numerical modelling is essentialto improve the quality of (or to shorten) design cycles and allow performance level enhancements in earlystages of development [135]. The goal is to afford simulations over very long times with many parameters orto embed a model in an alert system.

In addition to this, even in the best of circumstances, the reliability of numerical predictions is limitedby the intrinsic randomness of the data used in practice to define boundary conditions, initial conditions,geometry, etc. This uncertainty, related to the measurement errors, is defined as aleatory, and cannot beremoved, nor reduced. In addition, physical models and the related Partial Differential Equations (PDEs),feature a structural uncertainty, since they are derived with assumptions of limited validity and calibratedwith manipulated experimental data (filtering, averaging, etc ..). These uncertainties are defined as epistemic,as they are a deficiency due to a lack of knowledge [57], [124]. Unfortunately, measurements in fluids aredelicate and expensive. In complex flows, especially in flows involving interfaces and moving fronts, theyare sometimes impossible to carry out, due to scaling problems, repeatability issues (e.g. tsunami events),technical issues (different physics in the different flow regions) or dangerousness (e.g. high temperature reentryflows, or combustion). Frequently, they are impractical, due to the time scales involved (e.g. characterisationof oxidation processes related to a new material micro-/meso- structure [83]). This increases the amountof uncertainties associated to measurements and reduces the amount of information available to constructphysical/PDE models. These uncertainties play also a crucial role when one wants to deal with numericalcertification or optimization of a fluid based device. However, this makes the required number of flowsimulations grow as high as hundreds or even thousands of times. The associated costs are usually prohibitive.So the real challenge is to be able to construct an accurate and computationally affordable numerical modelhandling efficiently uncertainties. In particular, this model should be able to take into account the variabilitydue to uncertainties, those coming from the certification/optimization parameters as well as those coming frommodelling choices.

To face this challenge and provide new tools to accurately and robustly modelize and certify engineeringdevices based on fluid flows with moving fronts, we propose a program mixing scientific research inasymptotic PDE analysis, high order adaptive PDE discretizations and uncertainty quantification.

2.3. Our approachA standar way a certification study may be contacted can be described as two box modelling. The first box isthe physical model itself, which is composed of the 3 main elements: PDE system, mesh generation/adaptation,and discretization of the PDE (numerical scheme). The second box is the main robust certification loop whichcontains separate boxes involving the evaluation of the physical model, the post-processing of the output, andthe exploration of the spaces of physical and stochastic parameters (uncertainties). There are some knowninteractions taking place in the loop which are a necessary to exploit as much as possible the potential ofhigh order methods [103] such as e.g. h−/p−/r− adaptation in the physical model w.r.t. some post-processedoutput value, or w.r.t. some sort of adjoint sensitivity coming from the physical parameter evolution box, etc.As things stand today, we will not be able to take advantage of the potential of new high order numericaltechniques and of hierarchical (multi-fidelity) robust certification approaches without some very aggressiveadaptive methodology. Such a methodology, will require interactions between e.g. the uncertainty quantifica-tion methods and the adaptive spatial discretization, as well as with the PDE modelling part. Such a strategycannot be developed, let alone implemented in an operational context, without completely disassembling thescheme of the two boxes, and letting all the parts (PDE system, mesh generation/adaptation, numerical scheme,


evalutaion of the physical model, the post processing of the output, exploration of the spaces of physical andstochastic parameters) interact together. This is what we want to do in CARDAMOM . We have the unique com-bination of skills which allows to explore such an avenue: PDE analysis, high order numerical discretizations,mesh generation and adaptation, optimization and uncertainty quantification, specific issues related to theapplications considered.

Our strength is also our unique chance of exploring the interactions between all the parts. We will try to answersome fundamental questions related to the following aspects

• What are the relations between PDE model accuracy (asymptotic error) and scheme accuracy, andhow to control, en possibly exploit these relations to minimize the error for a given computationaleffort ;

• How to devise and implement adaptation techniques (r−, h−, and p−) for time dependent problemswhile guaranteeing an efficient time marching procedure (minimize CPU time at constant error) ;

• How to exploit the wide amount of information made available from the optimization and uncertaintyquantification process to construct a more aggressive adaptation strategy in physical, parameter, andstochastic space, and in the physical model itself ;

These research avenues related to the PDE models and numerical methods used, will allow us to have animpact on the applications communities targeted which are

• Aeronautics and aerospace engineering (de-anti icing systems, space re-entry) ;• Energy engineering (organic Rankine cycles and wave energy conversion) ;• Material engineering (self healing composite materials) ;• Coastal engineering (coastal protection, hazard assessment etc.).

The main research directions related to the above topics are discussed in the following section.

3. Research Program3.1. Variational discrete asymptotic modelling

In many of the applications we consider, intermediate fidelity models are or can be derived using an asymptoticexpansion for the relevant scale resolving PDEs, and eventually considering some averaged for of the resultingcontinuous equations. The resulting systems of PDEs are often very complex and their characterization, e.g.in terms of stability, unclear, or poor, or too complex to allow to obtain discrete analogy of the continuousproperties. This makes the numerical approximation of these PDE systems a real challenge. Moreover, mostof these models are often based on asymptotic expansions involving small geometrical scales. This is true formany applications considered here involving flows in/of thin layers (free surface waves, liquid films on wingsgenerating ice layers, oxide flows in material cracks, etc). This asymptotic expansion is nothing else than adiscretization (some sort of Taylor expansion) in terms of the small parameter. The actual discretization of thePDE system is another expansion in space involving as a small parameter the mesh size. What is the interactionbetween these two expansions ? Could we use the spatial discretization (truncation error) as means of filteringundesired small scales instead of having to explicitly derive PDEs for the large scales ? We will investigate indepth the relations between asymptotics and discretization by :

• comparing the asymptotic limits of discretized forms of the relevant scale resolving equations withthe discretization of the analogous continuous asymptotic PDEs. Can we discretize a well understoodsystem of PDEs instead of a less understood and more complex one ? ;

• study the asymptotic behaviour of error terms generated by coarse one-dimensional discretizationin the direction of the “small scale”. What is the influence of the number of cells along the verticaldirection, and of their clustering ? ;

• derive equivalent continuous equations (modified equations) for anisotropic discretizations in whichthe direction is direction of the “small scale” is approximated with a small number of cells. What isthe relation with known asymptotic PDE systems ?


Our objective is to gain sufficient control of the interaction between discretization and asymptotics to be ableto replace the coupling of several complex PDE systems by adaptive strongly anisotrotropic finite elementapproximations of relevant and well understood PDEs. Here the anisotropy is intended in the sense of havinga specific direction in which a much poorer (and possibly variable with the flow conditions) polynomialapproximation (expansion) is used. The final goal is, profiting from the availability of faster and cheapercomputational platforms, to be able to automatically control numerical and physical accuracy of the modelwith the same techniques. This activity will be used to improve our modelling in coastal engineering as wellas for de-anti icing systems, wave energy converters, composite materials (cf. next sections).

In parallel to these developments, we will make an effort in to gain a better understanding of continuousasymptotic PDE models. We will in particular work on improving, and possibly, simplifying their numericalapproximation. An effort will be done in trying to embed in these more complex nonlinear PDE modelsdiscrete analogs of operator identities necessary for stability (see e.g. the recent work of [106], [110] andreferences therein).

3.2. High order discretizations on moving adaptive meshesWe will work on both the improvement of high order mesh generation and adaptation techniques, and theconstruction of more efficient, adaptive high order discretisation methods.Concerning curved mesh generation, we will focus on two points. First propose a robust and automatic methodto generate curved simplicial meshes for realistic geometries. The untangling algorithm we plan to develop isa hybrid technique that gathers a local mesh optimization applied on the surface of the domain and a linearelasticity analogy applied in its volume. Second we plan to extend the method proposed in [60] to hybridmeshes (prism/tetra).

For time dependent adaptation we will try to exploit as much as possible the use of r−adaptation techniquesbased on the solution of some PDE system for the mesh. We will work on enhancing the initial results of [64],[66] by developing more robust nonlinear variants allowing to embed rapidly moving objects. For this the useof non-linear mesh PDEs (cf e.g. [120], [127], [76]), combined with Bezier type approximations for the meshdisplacements to accommodate high order curved meshes [60], and with improved algorithms to discretizeaccurately and fast the elliptic equations involved. For this we will explore different type of relaxation methods,including those proposed in [107], [113], [112] allowing to re-use high order discretizations techniques alreadyused for the flow variables. All these modelling approaches for the mesh movement are based on someminimization argument, and do not allow easily to take into account explicitly properties such as e.g. thepositivity of nodal volumes. An effort will be made to try to embed these properties, as well as to improvethe control on the local mesh sizes obtained. Developments made in numerical methods for Lagrangianhydrodynamics and compressible materials may be a possible path for these objectives (see e.g. [86], [133],[132] and references therein). We will stretch the use of these techniques as much as we can, and couple themwith remeshing algorithms based on local modifications plus conservative, high order, and monotone ALE (orother) remaps (cf. [61], [96], [134], [84] and references therein).The development of high order schemes for the discretization of the PDE will be a major part of our activity.We will work from the start in an Arbitrary Lagrangian Eulerian setting, so that mesh movement will be easilyaccommodated, and investigate the following main points:

• the ALE formulation is well adapted both to handle moving meshes, and to provide conservative,high order, and monotone remaps between different meshes. We want to address the issue of cost-accuracy of adaptive mesh computations by exploring different degrees of coupling between the flowand the mesh PDEs. Initial experience has indicated that a clever coupling may lead to a considerableCPU time reduction for a given resolution [66], [64]. This balance is certainly dependent on thenature of the PDEs, on the accuracy level sought, on the cost of the scheme, and on the timestepping technique. All these elements will be taken into account to try to provide the most efficientformulation ;


• the conservation of volume, and the subsequent preservation of constant mass-momentum-energystates on deforming domains is one of the most primordial elements of Arbitrary Lagrangian-Eulerian formulations. For complex PDEs as the ones considered here, of especially for someapplications, there may be a competition between the conservation of e.g. mass, an the conservationof other constant states, as important as mass. This is typically the case for free surface flows, inwhich mass preservation is in competitions with the preservation of constant free surface levels [65].Similar problems may arise in other applications. Possible solutions to this competition may comefrom super-approximation (use of higher order polynomials) of some of the data allowing to reduce(e.g. bathymetry) the error in the preservation of one of the competing quantities. This is similarto what is done in super-parametric approximations of the boundaries of an object immersed in theflow, except that in our case the data may enter the PDE explicitly and not only through the boundaryconditions. Several efficient solutions for this issue will be investigated to obtain fully conservativemoving mesh approaches:

• an issue related to the previous one is the accurate treatment of wall boundaries. It is known that evenfor standard lower order (second) methods, a higher order, curved, approximation of the boundariesmay be beneficial. This, however, may become difficult when considering moving objects, as in thecase e.g. of the study of the impact of ice debris in the flow. To alleviate this issue, we plan to followon with our initial work on the combined use of immersed boundaries techniques with high order,anisotropic (curved) mesh adaptation. In particular, we will develop combined approaches involvinghigh order hybrid meshes on fixed boundaries with the use of penalization techniques and immersedboundaries for moving objects. We plan to study the accuracy obtainable across discontinuousfunctions with r−adaptive techniques, and otherwise use whenever necessary anisotropic meshesto be able to provide a simplified high order description of the wall boundary (cf. [105]). The use ofpenalization will also provide a natural setting to compute immediate approximations of the forceson the immersed body [111], [114]. An effort will be also made on improving the accuracy of thesetechniques using e.g. higher order approaches, either based on generalizations of classical splittingmethods [97], or on some iterative Defect Correction method (see e.g. [78]) ;

• the proper treatment of different physics may be addressed by using mixed/hybrid schemes in whichdifferent variables/equations are approximated using a different polynomial expansion. A typicalexample is our work on the discretization of highly non-linear wave models [92] in which wehave shown how to use a standard continuous Galerkin method for the elliptic equation/variablerepresentative of the dispersive effects, while the underlying hyperbolic system is evolved using a(discontinuous) third order finite volume method. This technique will be generalized to other classesof discontinuous methods, and similar ideas will be used in other context to provide a flexibleapproximation. Such mathods have clear advantages in multiphase flows but not only. A typicalexample where such mixed methods are beneficial are flows involving different species and tracerequations, which are typically better treated with a discontinuous approximation. Another exampleis the use of this mixed approximation to describe the topography with a high order continuouspolynomial even in discontinuous method. This allows to greatly simplify the numerical treatmentof the bathymetric source terms ;

• the enhancement of stabilized methods based on some continuous finite element approximation willremain a main topic. We will further pursue the study on the construction of simplified stabilizationoperators which do not involve any contributions to the mass matrix. We will in particular generalizeour initial results [122], [63], [123] to higher order spatial approximations using cubature points,or Bezier polynomials, or also hierarchical approximations. This will also be combined with timedependent variants of the reconstruction techniques initially proposed by D. Caraeni [77], allowing tohave a more flexible approach similar to the so-called PnPm method [89], [126]. How to localize theseenhancements, and to efficiently perform local reconstructions/enrichment, as well as p−adaptation,and handling hanging nodes will also be a main line of work. A clever combination of hierarchicalenrichment of the polynomials, with a constrained approximation will be investigated. All thesedevelopments will be combined with the shock capturing/positivity preserving construction we


developed in the past. Other discontinuity resolving techniques will be investigated as well, suchas face limiting techniques as those partially studied in [94] ;

• time stepping is an important issue, especially in presence of local mesh adaptation. The techniqueswe use will force us to investigate local and multilevel techniques. We will study the possibilityconstructing semi-implicit methods combining extrapolation techniques with space-time variationalapproaches. Other techniques will be considered, as multi-stage type methods obtained using Defect-Correction, Multi-step Runge-Kutta methods [74], as well as spatial partitioning techniques [102].A major challenge will be to be able to guarantee sufficient locality to the time integration methodto allow to efficiently treat highly refined meshes, especially for viscous reactive flows. Anotherchallenge will be to embed these methods in the stabilized methods we will develop.

3.3. Coupled approximation/adaptation in parameter and physical spaceAs already remarked, classical methods for uncertainty quantification are affected by the so-called Curse-of-Dimensionality. Adaptive approaches proposed so far, are limited in terms of efficiency, or of accuracy. Ouraim here is to develop methods and algorithms permitting a very high-fidelity simulation in the physical andin the stochastic space at the same time. We will focus on both non-intrusive and intrusive approaches.

Simple non-intrusive techniques to reduce the overall cost of simulations under uncertainty will be based onadaptive quadrature in stochastic space with mesh adaptation in physical space using error monitors relatedto the variance of to the sensitivities obtained e.g. by an ANOVA decomposition. For steady state problems,remeshing using metric techniques is enough. For time dependent problems both mesh deformation and re-meshing techniques will be used. This approach may be easily used in multiple space dimensions to minimizethe overall cost of model evaluations by using high order moments of the properly chosen output functionalfor the adaptation (as in optimization). Also, for high order curved meshes, the use of high order momentsand sensitivities issued from the UQ method or optimization provides a viable solution to the lack of errorestimators for high order schemes.

Despite the coupling between stochastic and physical space, this approach can be made massively parallelby means of extrapolation/interpolation techniques for the high order moments, in time and on a referencemesh, guaranteeing the complete independence of deterministic simulations. This approach has the additionaladvantage of being feasible for several different application codes due to its non-intrusive character.To improve on the accuracy of the above methods, intrusive approaches will also be studied. To propagateuncertainties in stochastic differential equations, we will use Harten’s multiresolution framework, following[59]. This framework allows a reduction of the dimensionality of the discrete space of function representation,defined in a proper stochastic space. This reduction allows a reduction of the number of explicit evaluationsrequired to represent the function, and thus a gain in efficiency. Moreover, multiresolution analysis offers anatural tool to investigate the local regularity of a function and can be employed to build an efficient refinementstrategy, and also provides a procedure to refine/coarsen the stochastic space for unsteady problems. Thisstrategy should allow to capture and follow all types of flow structures, and, as proposed in [59], allows toformulate a non-linear scheme in terms of compression capabilities, which should allow to handle non-smoothproblems. The potential of the method also relies on its moderate intrusive behaviour, compared to e.g. spectralGalerkin projection, where a theoretical manipulation of the original system is needed.Several activities are planned to generalize our initial work, and to apply it to complex flows in multiple (space)dimensions and with many uncertain parameters.

The first is the improvement of the efficiency. This may be achieved by means of anisotropic mesh refinement,and by experimenting with a strong parallelization of the method. Concerning the first point, we will investigateseveral anisotropic refinement criteria existing in literature (also in the UQ framework), starting with thosealready used in the team to adapt the physical grid. Concerning the implementation, the scheme formulatedin [59] is conceived to be highly parallel due to the external cycle on the number of dimensions in the spaceof uncertain parameters. In principle, a number of parallel threads equal to the number of spatial cells couldbe employed. The scheme should be developed and tested for treating unsteady and discontinuous probabilitydensity function, and correlated random variables. Both the compression capabilities and the accuracy of the


scheme (in the stochastic space) should be enhanced with a high-order multidimensional conservative andnon-oscillatory polynomial reconstruction (ENO/WENO).

Another main objective is related to the use of multiresolution in both physical and stochastic space. Thisrequires a careful handling of data and an updated definition of the wavelet. Until now, only a weakcoupling has been performed, since the number of points in the stochastic space varies according to thephysical space, but the number of points in the physical space remains unchanged. Several works exist onthe multiresolution approach for image compression, but this could be the first time i in which this kind ofapproach would be applied at the same time in the two spaces with an unsteady procedure for refinement(and coarsening). The experimental code developed using these technologies will have to fully exploit theprocessing capabilities of modern massively parallel architectures, since there is a unique mesh to handle inthe coupled physical/stochastic space.

3.4. Robust multi-fidelity modelling for optimization and certificationDue to the computational cost, it is of prominent importance to consider multi-fidelity approaches gatheringhigh-fidelity and low-fidelity computations. Note that low-fidelity solutions can be given by both the useof surrogate models in the stochastic space, and/or eventually some simplified choices of physical modelsof some element of the system. Procedures which deal with optimization considering uncertainties forcomplex problems may require the evaluation of costly objective and constraint functions hundreds or eventhousands of times. The associated costs are usually prohibitive. For these reason, the robustness of the optimalsolution should be assessed, thus requiring the formulation of efficient methods for coupling optimization andstochastic spaces. Different approaches will be explored. Work will be developed along three axes:

1. a robust strategy using the statistics evaluation will be applied separately, i.e. using only low or high-fidelity evaluations. Some classical optimization algorithms will be used in this case. Influence ofhigh-order statistics and model reduction in the robust design optimization will be explored, also byfurther developing some low-cost methods for robust design optimization working on the so-calledSimplex2 method [82] ;

2. a multi-fidelity strategy by using in an efficient way low fidelity and high-fidelity estimators bothin physical and stochastic space will be conceived, by using a Bayesian framework for taking intoaccount model discrepancy and a PC expansion model for building a surrogate model ;

3. develop advanced methods for robust optimization. In particular, the Simplex2 method will bemodified for introducing a hierarchical refinement with the aim to reduce the number of stochasticsamples according to a given design in an adaptive way.

This work is related to the activities foreseen in the EU contract MIDWEST, in the ANR LabCom projectVIPER (currently under evaluation), in a joint project with DGA and VKI, in two projects under way withAIRBUS and SAFRAN-HERAKLES.

4. Application Domains

4.1. De-anti icing systemsImpact of large ice debris on downstream aerodynamic surfaces and ingestion by aft mounted engines must beconsidered during the aircraft certification process. It is typically the result of ice accumulation on unprotectedsurfaces, ice accretions downstream of ice protected areas, or ice growth on surfaces due to delayed activationof ice protection systems (IPS) or IPS failure. This raises the need for accurate ice trajectory simulation toolsto support pre-design, design and certification phases while improving cost efficiency. Present ice trajectorysimulation tools have limited capabilities due to the lack of appropriate experimental aerodynamic force andmoment data for ice fragments and the large number of variables that can affect the trajectories of ice particlesin the aircraft flow field like the shape, size, mass, initial velocity, shedding location, etc... There are generallytwo types of model used to track shed ice pieces. The first type of model makes the assumption that ice


pieces do not significantly affect the flow. The second type of model intends to take into account ice piecesinteracting with the flow. We are concerned with the second type of models, involving fully coupled time-accurate aerodynamic and flight mechanics simulations, and thus requiring the use of high efficiency adaptivetools, and possibly tools allowing to easily track moving objects in the flow. We will in particular pursueand enhance our initial work based on adaptive immerse boundary capturing of moving ice debris, whosemovements are computed using basic mechanical laws.

In [68] it has been proposed to model ice shedding trajectories by an innovative paradigm that is based onCArtesian grids, PEnalization and LEvel Sets (LESCAPE code). Our objective is to use the potential of highorder unstructured mesh adaptation and immersed boundary techniques to provide a geometrically flexibleextension of this idea. These activities will be linked to the development of efficient mesh adaptation andtime stepping techniques for time dependent flows, and their coupling with the immersed boundary methodswe started developing in the FP7 EU project STORM [58], [114]. In these methods we compensate for theerror at solid walls introduced by the penalization by using anisotropic mesh adaptation [87], [104], [105].From the numerical point of view one of the major challenges is to guarantee efficiency and accuracy of thetime stepping in presence of highly stretched adaptive and moving meshes. Semi-implicit, locally implicit,multi-level, and split discretizations will be explored to this end.Besides the numerical aspects, we will deal with modelling challenges. One source of complexity is theinitial conditions which are essential to compute ice shedding trajectories. It is thus extremely important tounderstand the mechanisms of ice release. With the development of next generations of engines and aircraft,there is a crucial need to better assess and predict icing aspects early in design phases and identify breakthroughtechnologies for ice protection systems compatible with future architectures. When a thermal ice protectionsystem is activated, it melts a part of the ice in contact with the surface, creating a liquid water film andtherefore lowering ability of the ice block to adhere to the surface. The aerodynamic forces are then able todetach the ice block from the surface [70]. In order to assess the performance of such a system, it is essential tounderstand the mechanisms by which the aerodynamic forces manage to detach the ice. The current state of theart in icing codes is an empirical criterion. However such an empirical criterion is unsatisfactory. Following theearly work of [72], [67] we will develop appropriate asymptotic PDE approximations allowing to describe theice formation and detachment, trying to embed in this description elements from damage/fracture mechanics.These models will constitute closures for aerodynamics/RANS and URANS simulations in the form of PDEwall models, or modified boundary conditions.In addition to this, several sources of uncertainties are associated to the ice geometry, size, orientation andthe shedding location. In very few papers [118], some sensitivity analysis based on Monte Carlo method havebeen conducted to take into account the uncertainties of the initial conditions and the chaotic nature of theice particle motion. We aim to propose some systematic approach to handle every source of uncertainty in anefficient way relying on some state-of-art techniques developed in the Team. In particular, we will performan uncertainty propagation of some uncertainties on the initial conditions (position, orientation, velocity,...)through a low-fidelity model in order to get statistics of a multitude of particle tracks. This study will be donein collaboration with ETS (Ecole de Technologies Supérieure, Canada). The longterm objective is to producefootprint maps and to analyse the sensitivity of the models developed.

4.2. Space re-entryAs already mentioned, atmospheric re-entry involves multi-scale fluid flow physics including highly rarefiedeffects, aerothermochemistry, radiation. All this must be coupled to the response of thermal protectionmaterials to extreme conditions. This response is most often the actual objective of the study, to allow thecertification of Thermal Protection Systems (TPS).


One of the applications we will consider is the so-called post-flight analysis of a space mission. This involvesreconstructing the history of the re-entry module (trajectory and flow) from data measured on the spacecraftby means of a Flush Air Data System (FADS), a set of sensors flush mounted in the thermal protectionsystem to measure the static pressure (pressure taps) and heat flux (calorimeters). This study involves theaccurate determination of the freestream conditions during the trajectory. In practice this means determiningtemperature, pressure, and Mach number in front of the bow shock forming during re-entry. As shown byzur Nieden and Olivier [136], state of the art techniques for freestream characterization rely on severalapproximations, such as e.g. using an equivalent calorically perfect gas formulas instead of taking into accountthe complex aero-thermo-chemical behaviour of the fluid. These techniques do not integrate measurementerrors nor the heat flux contribution, for which a correct knowledge drives more complex models such as gassurface interaction. In this context, CFD supplied with UQ tools permits to take into account chemical effectsand to include both measurement errors and epistemic uncertainties, e.g. those due to the fluid approximation,on the chemical model parameters in the bulk and at the wall (surface catalysis).

Rebuilding the freestream conditions from the stagnation point data therefore amounts to solving a stochasticinverse problem, as in robust optimization. Our objective is to build a robust and global framework forrebuilding freestream conditions from stagnation-point measurements for the trajectory of a re-entry vehicle.To achieve this goal, methods should be developed for

• an accurate simulation of the flow in all the regimes, from rarefied, to transitional, to continuous ;• providing a complete analysis about the reliability and the prediction of the numerical simulation

in hypersonic flows, determining the most important source of error in the simulation (PDE model,discretization, mesh, etc)

• reducing the overall computational cost of the analysis .

Our work on the improvement of the simulation capabilities for re-entry flows will focus both on the modelsand on the methods. We will in particular provide an approach to extend the use of standard CFD models inthe transitional regime, with CPU gains of several orders of magnitude w.r.t. Boltzmann solvers. To do thiswe will use the results of a boundary layer analysis allowing to correct the Navier-Stokes equations. Thistheory gives modified (or extended) boundary conditions that are called "slip velocity" and "temperaturejump" conditions. This theory seems to be completely ignored by the aerospace engineering community.Instead, people rather use a simpler theory due to Maxwell that also gives slip and jump boundary conditions:however, the coefficients given by this theory are not correct. This is why several teams have tried to modifythese coefficients by some empirical methods, but it seems that this does not give any satisfactory boundaryconditions.

Our project is twofold. First, we want to revisit the asymptotic theory, and to make it known in the aerospacecommunity. Second, we want to make an intensive sensitivity analysis of the model to the various coefficientsof the boundary conditions. Indeed, there are two kinds of coefficients in these boundary conditions. Thefirst one is the accomodation coefficient: in the kinetic model, it gives the proportion of molecules that arespecularly reflected, while the others are reflected according to a normal distribution (the so-called diffusereflexion). This coefficient is a data of the kinetic model that can be measured by experiments: it depends onthe material and the structure of the solid boundary, and of the gas. Its influence on the results of a Navier-Stokes simulation is certainly quite important. The other coefficients are those of the slip and jump boundaryconditions: they are issued from the boundary layer analysis, and we have absolutely no idea of the order ofmagnitude of their influence on the results of a Navier-Stokes solution. In particular, it is not clear if theseresults are more sensitive to the accomodation coefficient or to these slip and jump coefficients.

In this project, we shall make use of the expertise of the team on uncertainty quantification to investigatethe sensitivity of the Navier-Stokes model with slip and jump coefficients to these various coefficients. Thiswould be rather new in the field of aerospace community. It could also have some impacts in other sciencesin which slip and jump boundary conditions with incorrect coefficients are still used, like for instance in spraysimulations: for very small particles immersed in a gas, the drag coefficient is modified to account for rarefiedeffects (when the radius of the particle is of the same order of magnitude as the mean free path in the gas), andslip and jump boundary conditions are used.


Another application which has very close similarities to the physics of de-anti icing systems is the modellingof the solid and liquid ablation of the thermal protective system of the aircraft. This involves the degradationand recession of the solid boundary of the protection layer due to the heating generated by the friction. Asin the case of de-anti icing systems, the simulation of these phenomena need to take into account the heatconduction in the solid, its phase change, and the coupling between a weakly compressible and a compressiblephase. Fluid/Solid coupling methods are generally based on a weak approach. Here we will both study, bytheoretical and numerical techniques, a strong coupling method for the interaction between the fluid and thesolid, and, as for de-anti icing systems, attempt at developing appropriate asymptotic models. These wouldconstitute some sort of thin layer/wall models to couple to the external flow solver.

These modelling capabilities will be coupled to high order adaptive discretizations to provide high fidelity flowmodels. One of the most challenging problems is the minimization of the influence of mesh and scheme on thewall conditions on the re-entry module. To reduce this influence, we will investigate both high order adaptationacross the bow shock, and possibly adaptation based on uncertainty quantification high order moments relatedto the heat flux estimation, or shock fitting techniques [71], [109]. These tools will be coupled to our robustinverse techniques. One of our objectives is to development of a low-cost strategy for improving the numericalprediction by taking into account experimental data. Some methods have been recently introduced [117] forproviding an estimation of the numerical errors/uncertainties. We will use some metamodels for solving theinverse problem, by considering all sources of uncertainty, including those on physical models. We willvalidate the framework sing the experimental data available in strong collaboration with the von KarmanInstitute for Fluid dynamics (VKI). In particular, data coming from the VKI Longshot facility will be used.We will show application of the developed numerical tool for the prediction in flight conditions.

These activities will benefit from our strong collaborations with the CEA and with the von Karman Institutefor Fluid Dynamics and ESA.

4.3. EnergyWe will develop modelling and design tools, as well as dedicated platforms, for Rankine cycles using complexfluids (organic compounds), and for wave energy extraction systems.Organic Rankine Cycles (ORCs) use heavy organic compounds as working fluids. This results in superiorefficiency over steam Rankine cycles for source temperatures below 900 K. ORCs typically require onlya single-stage rotating component making them much simpler than typical multi-stage steam turbines. Thestrong pressure reduction in the turbine may lead to supersonic flows in the rotor, and thus to the appearanceof shocks, which reduces the efficiency due to the associated losses. To avoid this, either a larger multi stageinstallation is used, in which smaller pressure drops are obtained in each stage, or centripetal turbines are used,at very high rotation speeds (of the order of 25,000 rpm). The second solution allows to keep the simplicity ofthe expander, but leads to poor turbine efficiencies (60-80%) - w.r.t. modern, highly optimized, steam and gasturbines - and to higher mechanical constraints. The use of dense-gas working fluids, i.e. operating close tothe saturation curve, in properly chosen conditions could increase the turbine critical Mach number avoidingthe formation of shocks, and increasing the efficiency. Specific shape optimization may enhance these effects,possibly allowing the reduction of rotation speeds. However, dense gases may have significantly differentproperties with respect to dilute ones. Their dynamics is governed by a thermodynamic parameter known asthe fundamental derivative of gas dynamics

Γ = 1 +ρ

c

(∂c

∂ρ

)s

, (1)

where ρ is the density, c is the speed of sound and s is the entropy. For ideal gas Γ = (γ + 1)/2 > 1. For somecomplex fluids and some particular conditions of pressure and temperature, Γ may be lower that one, implyingthat (∂c/∂ρ)s < 0. This means that the acceleration of pressure perturbations through a variable density fluidsmay be reversed and become a deceleration. It has been shown that, for Γ << 1, compression shocks arestrongly reduced, thus alleviating the shock intensity. This has great potential in increasing the efficiency. Thisis why so much interest is put on dense gas ORCs.


The simulation of these gases requires accurate thermodynamic models, such as Span-Wagner or Peng-Robinson (see [80]). The data to build these models is scarce due to the difficulty of performing reliableexperiments. The related uncertainty is thus very high. Our work will go in the following directions:

1. develop deterministic models for the turbine and the other elements of the cycle. These will involvemulti-dimensional high fidelity, as well as intermediate and low fidelity (one- and zero-dimensional),models for the turbine, and some 0D/1D models for other element of the cycle (pump, condenser,etc) ;

2. validation of the coupling between the various elements. The following aspects will be considered:characterization of the uncertainties on the cycle components (e.g. empirical coefficients modellingthe pump or the condenser), calibration of the thermodynamic parameters, model the uncertainty ofeach element, and the influence of the unsteady experimental data ;

3. demonstrate the interest of a specific optimization of geometry, operating conditions, and the choiceof the fluid, according to the geographical location by including local solar radiation data. Multi-objective optimization will be considered to maximize performance indexes (e.g. Carnot efficiency,mechanical work and energy production), and to reduce the variability of the output.

This work will provide modern tools for the robust design of ORCs systems. It benefits from the directcollaboration with the SME EXOES (ANR LAbCom VIPER), and from a collaboration with LEMMA.Wave energy conversion is an emerging sector in energy engineering. The design of new and efficient WaveEnergy Converters (WECs) is thus a crucial activity. As pointed out by Weber [135], it is more economical toraise the technology performance level (TPL) of a wave energy converter concept at low technology readinesslevel (TRL). Such a development path puts a greater demand on the numerical methods used. The findings ofWeber also tell us that important design decisions as well as optimization should be performed as early in thedevelopment process as possible. However, as already mentioned, today the wave energy sector relies heavilyon the use of tools based on simplified linear hydrodynamic models for the prediction of motions, loads, andpower production. Our objective is to provide this sector, and especially SMEs, with robust design tools tominimize the uncertainties in predicted power production, loads, and costs of wave energy.

Following our initial work [91], we will develop, analyse, compare, and use for multi-fidelityoptimization,non-linear models of different scales (fidelity) ranging from simple linear hydrodynamicsover asymptotic discrete nonlinear wave models, to non-hydrostatic anisoptropic Euler free surface solvers.We will not work on the development of small scale models (VOF-RANS or LES) but may use such models,developed by our collaborators, for validation purposes. These developments will benefit from all ourmethodological work on asymptotic modelling and high order discretizations. As shown in [91], asymptoticmodels foe WECs involve an equation for the pressure on the body inducing a PDE structure similar to thatof incompressible flow equations. The study of appropriate stable and efficient high order approximations(coupling velocity-pressure, efficient time stepping) will be an important part of this activity. Moreover, theflow-floating body interaction formulation introduces time stepping issues similar to those encountered influid structure interaction problems, and require a clever handling of complex floater geometries based onadaptive and ALE techniques. For this application, the derivation of fully discrete asymptotics may actuallysimplify our task.

Once available, we will use this hierarchy of models to investigate and identify the modelling errors, andprovide a more certain estimate of the cost of wave energy. Subsequently we will look into optimizationcycles by comparing time-to-decision in a multi-fidelity optimization context. In particular, this task willinclude the development and implementation of appropriate surrogate models to reduce the computationalcost of expensive high fidelity models. Here especially artificial neural networks (ANN) and Kriging responsesurfaces (KRS) will be investigated. This activity on asymptotic non-linear modelling for WECs, which hashad very little attention in the past, will provide entirely new tools for this application. Multi-fidelity robustoptimization is also an approach which has never been applied to WECs.

This work is the core of the EU OCEANEranet MIDWEST project, which we coordinate. It will be performedin collaboration with our European partners, and with a close supervision of European SMEs in the sector,which are part of the steering board of MIDWEST (WaveDragon, Waves4Power, Tecnalia).


4.4. Materials engineeringBecause of their high strength and low weight, ceramic-matrix composite materials (CMCs) are the focusof active research for aerospace and energy applications involving high temperatures, either military orcivil. Though based on brittle ceramic components, these composites are not brittle due to the use of afibre/matrix interphase that preserves the fibres from cracks appearing in the matrix. Recent developments aimat implementing also in civil aero engines a specific class of Ceramic Matrix Composite materials (CMCs) thatshow a self-healing behaviour. Self-healing consists in filling cracks appearing in the material with a densefluid formed in-situ by oxidation of part of the matrix components. Self-healing (SH) CMCs are composed ofa complex three-dimensional topology of woven fabrics containing fibre bundles immersed in a matrix coatingof different phases. The oxide seal protects the fibres which are sensitive to oxidation, thus delaying failure.The obtained lifetimes reach hundreds of thousands of hours [121].

The behaviour of a fibre bundle is actually extremely variable, as the oxidation reactions generating theself-healing mechanism have kinetics strongly dependent on temperature and composition. In particular,the lifetime of SH-CMCs depends on: (i) temperature and composition of the surrounding atmosphere;(ii) composition and topology of the matrix layers; (iii) the competition of the multidimensional diffu-sion/oxidation/volatilization processes; (iv) the multidimensional flow of the oxide in the crack; (v) the innertopology of fibre bundles; (vi) the distribution of critical defects in the fibres. Unfortunately, experimentalinvestigations on the full materials are too long (they can last years) and their output too qualitative (the cou-pled effects can only be observed a-posteriori on a broken sample). Modelling is thus essential to study and todesign SH-CMCs.

In collaboration wit the LCTS laboratory (a joint CNRS-CEA-SAFRAN-Bordeaux University lab devotedto the study of thermo-structural materials in Bordeaux), we are developing a multi-scale model in which astructural mechanics solver is coupled with a closure model for the crack physico chemistry. This model isobtained as a multi-dimensional asymptotic crack averaged approximation fo the transport equations (Fick’slaws) with chemical reactions sources, plus a potential model for the flow of oxide [83], [88], [119]. Wehave demonstrated the potential of this model in showing the importance of taking into account the multi-dimensional topology of a fibre bundle (distribution of fibres) in the rupture mechanism. This means that the0-dimensional model used in most of the studies (se e.g. [79]) will underestimate appreciably the lifetime ofthe material. Based on these recent advances, we will further pursue the development of multi-scale multi-dimensional asymptotic closure models for the parametric design of self healing CMCs. Our objectives are toprovide: (i) new, non-linear multi-dimensional mathematical model of CMCs, in which the physico-chemistryof the self-healing process is more strongly coupled to the two-phase (liquid gas) hydro-dynamics of thehealing oxide ; (ii) a model to represent and couple crack networks ; (iii) a robust and efficient couplingwith the structural mechanics code ; (iv) validate this platform with experimental data obtained at the LCTSlaboratory. The final objective is to set up a multi-scale platform for the robust prediction of lifetime of SH-CMCs, which will be a helpful tool for the tailoring of the next generation of these materials.

4.5. Coastal and civil engineeringOur objective is to bridge the gap between the development of high order adaptive methods, which hasmainly been performed in the industrial context and environmental applications, with particular attention tocoastal and hydraulic engineering. We want to provide tools for adaptive non-linear modelling at large andintermediate scales (near shore, estuarine and river hydrodynamics). We will develop multi-scale adaptivemodels for free surface hydrodynamics. Beside the models and codes themselves, based on the most advancednumerics we will develop during this project, we want to provide sufficient know how to control, adapt andoptimize these tools.

We will focus our effort in the understanding of the interactions between asymptotic approximations andnumerical approximations. This is extremely important in at least two aspects. The first is the capabilityof a numerical model to handle highly dispersive wave propagation. This is usually done by high accuracyasymptotic PDE expansions. Here we plan to make heavily use of our results concerning the relations between


vertical asymptotic expansions and standard finite element approximations. In particular, we will investsome effort in the development of xy+z adaptive finite element approximations of the incompressible Eulerequations. Local p−adaptation of the vertical approximation may provide a “variable depth” approximationexploiting numerics instead of analytical asymptotics to control the physical behaviour of the model.

Another important aspect which is not understood well enough at the moment is the role of dissipation inwave breaking regions. There are several examples of breaking closure, going from algebraic and PDE-based eddy viscosity methods [101], [125], [116], [85], to hybrid methods coupling dispersive PDEs withhyperbolic ones, and trying to mimic wave breaking with travelling bores [129], [130], [128], [99], [92]. Inboth cases, numerical dissipation plays an important role and the activation or not of the breaking closure,as the quantitative contribution of numerical dissipation to the flow has not been properly investigated. Theseelements must be clarified to allow full control of adaptive techniques for the models used in this type ofapplications.

Another point we want to clarify is how to optimize the discretization of asymptotic PDE models. In particular,when adding mesh size(s) and time step, we are in presence of at least 3 (or even more) small parameters. Therelations between physical ones have been more or less investigates, as have been the ones between purelynumerical ones. We plan to study the impact of numerics on asymptotic PDE modelling by reverting the usualprocess and studying asymptotic limits of finite element discretizations of the Euler equations. Preliminaryresults show that this does allow to provide some understanding of this interaction and to possibly proposeconsiderably improved numerical methods [69].

5. New Software and Platforms

5.1. AeroSolParticipants: Simon Delmas [Universit de Bordeaux], Sbastien de Brye [Universit de Bordeaux], BenjaminLux [Cagire], Nikolaos Pattakos [Cardamom], Vincent Perrier [Cagire, correspondent], Mario Ricchiuto[Cardamom].

Developed since 2011 by V. Perrier in partnership with the Cardamom Inria team, the AeroSol library is a highorder finite element library written in C++. The code design has been carried for being able to perform efficientcomputations, with continuous and discontinuous finite element methods on hybrid and possibly curvilinearmeshes.

The work of the Cardamom team is focused on continuous finite element methods, while we focus ondiscontinuous Galerkin methods. However, everything is done for sharing the largest possible part of code.The distribution of the unknowns is made with the software PaMPA, first developed within the Inria teamsBacchus and Castor, and currently maintained in the Tadaam team.

The generic features of the library are Adaptive wall treatment for a second moment closure in the industrialcontext

• High order. It can be theoretically any order of accuracy, but the finite element basis, and quadratureformula are implemented for having up to a fifth order of accuracy.

• Hybrid and curvilinear meshes. AeroSol can deal with up to fifth order conformal meshescomposed of lines, triangles, quadrangles, tetrahedra, hexahedra, prism, and pyramids.

• Continuous and discontinuous discretization. AeroSol deals with both continuous and discontin-uous finite element methods.


We would like to emphasize three assets of this library:• Its development environment For allowing a good collaborative work and a functional library, a

strong emphasis has been put on the use of modern collaborative tools for developing our software.This includes the active use of a repository, the use of CMake for the compilation, the constantdevelopment of unitary and functional tests for all the parts of the library (using CTest), and theuse of the continuous integration tool Jenkins for testing the different configurations of AeroSol andits dependencies. Efficiency is regularly tested with direct interfacing with the PAPI library or withtools like scalasca.

• Its genericity A lot of classes are common to all the discretization, for example classes concerningI/O, finite element functions, quadrature, geometry, time integration, linear solver, models andinterface with PaMPA. Adding simple features (e.g. models, numerical flux, finite element basisor quadrature formula) can be easily done by writing the class, and declaring its use in only oneclass of the code.

• Its efficiency This modularity is achieved by means of template abstraction for keeping goodperformances. Dedicated efficient implementation, based on the data locality of the discontinuousGalerkin method has been developed. As far as parallelism is concerned, we use point-to-pointcommunications, the HDF5 library for parallel I/O. The behavior of the AeroSol library at mediumscale (1000 to 2000 cores) was studied in [108].

The AeroSol project fits with the first axis of the Bordeaux Sud Ouest development strategy, which is to builda coherent software suite scalable and efficient on new architectures, as the AeroSol library relies on severaltools developed in other Inria teams, especially for the management of the parallel aspects. At the end of 2015,AeroSol had the following features:

• Boundary conditions Periodic boundary conditions, time-dependent inlet and outlet boundary con-ditions. Adiabatic wall and isothermal wall. Steger-Warming based boundary condition. SyntheticEddy Method for generating turbulence.

• C++/Fortran interface Tests for binding fortran with C++.• Development environment An upgraded use of CMake for compilation (gcc, icc and xlc), CTest for

automatic tests and memory checking, lcov and gcov for code coverage reports. A CDash server forcollecting the unitary tests and the memory checking. An under development interface for functionaltests. Optional linking with HDF5, PAPI, with dense small matrices libraries (BLAS, Eigen). Anupdated shared project Plafrim and joint project Aerosol/Scotch/PaMPA project on the continuousintegration platform. An on-going integration of SPack for handling dependencies. A fixed ESSLinterface.

• Finite elements up to fourth degree for Lagrange finite elements and hierarchical orthogonal finiteelement basis (with Dubiner transform on simplices) on lines, triangles, quadrangles, tetrahedra,prisms, hexaedra and pyramids. Finite element basis that are interpolation basis on Gauss-Legendrepoints for lines, quadrangles, and hexaedra, and triangle (only 1st and 2nd order).

• Geometry Elementary geometrical functions for first order lines, triangles, quadrangles, prisms,tetrahedra, hexaedra and pyramids. Handling of high order meshes.

• In/Out Link with the XML library for handling with parameter files. Parallel reader for GMSH,with an embedded geometrical pre-partitioner. Writer on the VTK-ASCII legacy format (cell andpoint centered). Parallel output in vtu and pvtu (Paraview) for cell-centered visualization, andXDMF/HDF5 format for both cell and point centered visualization. Ability of saving the highorder solution and restarting from it. Computation of volumic and probe statistics. Ability of savingaveraged layer data in quad and hexa meshes. Ability of defining user defined output visualizationvariables.

• Instrumentation Aerosol can give some traces on memory consumption/problems with an interfac-ing with the PAPI library. Tests have also been performed with VTUNE and TAU. Tests with Maqaoand Scalasca (VIHPS workshop).


• Linear Solvers Link with the external linear solver UMFPack, PETSc and MUMPS. Internal solverfor diagonal and block-diagonal matrices.

• Memory handling discontinuous and continuous, sequential and parallel discretizations based onPaMPA for generic meshes, including hybrid meshes.

• Models Perfect gas Euler system, real gas Euler system (template based abstraction for a genericequation of state), scalar advection, Waves equation in first order formulation, generic interface fordefining space-time models from space models. Diffusive models: isotropic and anisotropic dif-fusion, compressible Navier-Stokes. Scalar advection-diffusion model. Linearized Euler equations,and Sutherland model for non isothermal diffusive flows. Shallow-water model.

• Multigrid Development of p-multigrid methods. This includes also the possibility of beginning acomputation with an order and to decrease or increase the order of approximation when restarting.For the p multigrid methods, V and W cycle have been developed, and restriction and prolongationopertors have also been developed. In progress implementation of h-multigrid, with the developmentof tests of the aggregation methods of PaMPA, and the definition of finite element basis on arbitrarycells.

• Numerical fluxes Centered fluxes, exact Godunov’ flux for linear hyperbolic systems, and Lax-Friedrich flux. Riemann solvers for Low Mach flows. Numerical flux accurate for steady andunsteady computations.

• Numerical schemes Continuous Galerkin method for the Laplace problem (up to fifth order) withnon consistent time iteration or with direct matrix inversion. Explicit and implicit discontinuousGalerkin methods for hyperbolic systems, diffusive and advection-diffusion problems. In progressoptimization by stocking the geometry for advection problems. SUPG and Residual distributionschemes. Optimization of DG schemes for advection-diffusion problems: stocking of the geometryand use of BLAS for all the linear phases of the scheme.

• Parallel computing Mesh redistribution, computation of Overlap with PaMPA. Collective asyn-chronous communications (PaMPA based). Asynchronous point to point communications. Tests onthe cluster Avakas from MCIA, and on Mésocentre de Marseille, and PlaFRIM. Tier-1 Turing (Blue-Gene). Weighted load balancing for hybrid meshes.

• Postprocessing High order projections over line postprocessing, possibility of stocking averageddata, such as the average flow and the Reynolds stresses.

• Quadrature formula up to 11th order for Lines, Quadrangles, Hexaedra, Pyramids, Prisms, up to14th order for tetrahedron, up to 21st order for triangles. Gauss-Lobatto type quadrature formula forlines, triangles, quadrangles and hexaedra.

• Time iteration explicit Runge-Kutta up to fourth order, explicit Strong Stability Preserving schemesup to third order. Optimized CFL time schemes: SSP(2,3) and SSP(3,4). CFL time stepping. Implicitintegration with BDF schemes from 2nd to 6th order Newton method for stationary problems.Implicit unstationary time iterator non consistent in time for stationary problems. Implementationof in house GMRES and conjugate gradient based on Jacobian free iterations.

• Validation Poiseuille, Taylor-Green vortex. Laplace equation on a ring and Poiseuille flow on aring. Volumic forcing based on wall dissipation.Turbulent channel flow.

In 2016, the following features have been added:• Geometric multigrid methods: aggregation of the mesh based on PaMPA, definition of finite element

basis on arbitrary shape cells. Definition of geometry, quadratures and numerical schemes onaggregated finite elements.

• Sutherland law in the Navier-Stokes equations.• Mass matrix free implementation of discontinuous Galerkin methods.• Improvement of installation documentation. Spack based installation.• Implementation of Boussinesq type models and Shallow water discretizations with well balancing,

positivity preserving, wet-dry handling, limiters based on entropy viscosity,• Implementation of Barotropic Euler equations• Implementation of Taylor-based basis on simplices.


5.2. CAKEKEYWORDS: Moving bodies, Rarefied flows

• Contact: Luc Mieussens

• URL: http://www.cake-solver.com/

FUNCTIONAL DESCRIPTION

Cake (Cut cell Algorithm for Kinetic Equations) can simulate 2D plane rarefied flows around movingobstacles, by using an immersed boundary technique with Cartesian grids. This code can simulate flowsinduced by temperature gradients, like the thermal creep flow. It has for instance been applied to the simulationof the Crookes radiometer.

5.3. CrysaKEYWORDS: Image processing, structural analysis, 2D crystallography

• Participants: Jean Mercat and Cécile Dobrzynski

• Partners: ISM - LCPO - LCTS (UMR 5801)

• Contact: Cécile Dobrzynski

Crysa is a library allowing to study the organization of objects once placed in an hexagonal grid thus allowingto analyze the crystal structure/organization of an image. The library allows to detect regions of coherencein an image of crystals, and it allows to determine e.g. the good separation of objects in an experiment (newpolymeric materials, plasma, ...).

5.4. Cut-ANOVAKEYWORDS: Stochastic models - Uncertainty quantification

• Participants: Pietro-Marco Congedo

• Contact: Pietro-Marco Congedo

SCIENTIFIC DESCRIPTION

An anchored analysis of variance (ANOVA) method is proposed to decompose the statistical moments.Compared to the standard ANOVA with mutually orthogonal component functions, the anchored ANOVA,with an arbitrary choice of the anchor point, loses the orthogonality if employing the same measure. However,an advantage of the anchored ANOVA consists in the considerably reduced number of deterministic solver’scomputations, which renders the uncertainty quantification of real engineering problems much easier. Differentfrom existing methods, the covariance decomposition of the output variance is used in this work to take accountof the interactions between non-orthogonal components, yielding an exact variance expansion and thus, witha suitable numerical integration method, provides a strategy that converges. This convergence is verified bystudying academic tests. In particular, the sensitivity problem of existing methods to the choice of anchor pointis analyzed via the Ishigami case, and we point out that covariance decomposition survives from this issue.Also, with a truncated anchored ANOVA expansion, numerical results prove that the proposed approach isless sensitive to the anchor point. The covariance-based sensitivity indices (SI) are also used, compared tothe variance-based SI. Furthermore, we emphasize that the covariance decomposition can be generalized in astraightforward way to decompose higher-order moments. For academic problems, results show the methodconverges to exact solution regarding both the skewness and kurtosis. The proposed method can indeed beapplied to a large number of engineering problems.FUNCTIONAL DESCRIPTION

http://www.cake-solver.com/


The Cut-ANOVA code (Fortran 90, MPI + OpenMP) is devoted to the stochastic analysis of numericalsimulations. The method implemented is based on the spectral expansion of "anchored ANOVA", allowing thecovariance-based sensitivity analysis. Compared to the conventional Sobol method, "Cut-ANOVA" providesthree sensitivity indices instead of one, which allows a better analysis of the reliability of the numericalprediction. On the other hand, "Cut-ANOVA" is able to compute the higher order statistical moments such asthe Skewness (3-rd order moment) and Kurtosis (4-th order moment). Several dimension reduction techniqueshave also been implemented to reduce the computational cost. Finally, thanks to the innovative methodimplemented into the Code Cut-ANOVA, one can obtain a similar accuracy for stochastic quantities by usinga considerably less number of deterministic model evaluations, compared with the classical Monte Carlomethod.

5.5. FmgKEYWORDS: Mesh adaptation, mesh deformation, elasticity, laplacian mesh equation

• Participants: Cécile Dobrzynski, Mario Ricchiuto, Leo Nouveau and Luca Arpaia



FMG is a library deforming an input/reference simplicial mesh w.r.t. a given smoothness error monitor(function gradient or Hessian), metric field, or given mesh size distribution. Displacements are computedby solving an elliptic Laplacian type equation with a continuous finite element method. The library returns anadapted mesh with a corresponding projected solution, obtained by either a second order projection, or by anALE finite element remap. This year a new semi-linear elasticity formulation has been implemented involvinga constant coefficient PDE with a nonlinear force accounting for the smoothness of the target function. Theadvantage of this approach is that the non-linearity does not influence the elastic differential operator thusleading to a description of the deformation governed by a time-invariant matrix even in unsteady simulations.Other developments currently implemented in SLOWS are being imported in FMG.

5.6. MMG3DKEYWORDS: Mesh - Anisotropic - Mesh adaptation

• Participants: Cécile Dobrzynski, Pascal Frey, Charles Dapogny and Algiane Froehly

• Partners: CNRS - IPB - Université de Bordeaux - UPMC


• URL: http://www.mmgtools.org


Mmg3d is an open source software for tetrahedral remeshing. It performs local mesh modifications. The meshis iteratively modified until the user prescriptions satisfaction.

Mmg3d can be used by command line or using the library version (C, C++ and Fortran API) : - It is a newversion af the MMG3D4 software. It remesh both the volume and surface mesh of a tetrahedral mesh. Itperforms isotropic and anisotropic mesh adaptation and isovalue discretization of a level-set function.

Mmg3d allows to control the boundaries approximation: The "ideal" geometry is reconstruct from thepiecewise linear mesh using cubic Bezier triangular partches. The surface mesh is modified to respect amaximal Hausdorff distance between the ideal geometry and the mesh.

Inside the volume, the software perform local mesh modifications ( such as edge swap, pattern split, isotropicand anisotropic Delaunay insertion...).FUNCTIONAL DESCRIPTION

Mmg3d is one of the software of the Mmg platform. Is is dedicated to the modification of 3D volume meshes.It perform the adaptation and the optimization of a tetrahedral mesh and allow to discretize an isovalue.

http://www.mmgtools.org


Mmg3d perform local mesh modifications. The mesh is iteratively modified until the user prescriptionsatisfaction.

5.7. Mmg platformKEYWORDS: Mesh - Mesh generation - Anisotropic - Mesh adaptation - Isovalue discretization

• Participants: Cécile Dobrzynski, Charles Dapogny, Pascal Frey and Algiane Froehly

• Partners: CNRS - IPB - Université de Bordeaux - UPMC


• URL: http://www.mmgtools.org


The Mmg platform gathers open source software for two-dimensional, surface and volume remeshing.The platform software perform local mesh modifications. The mesh is iteratively modified until the userprescriptions satisfaction.

The 3 softwares can be used by command line or using the library version (C, C++ and Fortran API) : -Mmg2d performs mesh generation and isotropic and anisotropic mesh adaptation. - Mmgs allows isotropicand anisotropic mesh adaptation for 3D surface meshes. - Mmg3d is a new version af the MMG3D4 software.It remesh both the volume and surface mesh of a tetrahedral mesh. It performs isotropic and anisotropic meshadaptation and isovalue discretization of a level-set function.

The platform software allow to control the boundaries approximation: The "ideal" geometry is reconstructfrom the piecewise linear mesh using cubic Bezier triangular partches. The surface mesh is modified to respecta maximal Hausdorff distance between the ideal geometry and the mesh.

Inside the volume, the software perform local mesh modifications ( such as edge swap, pattern split, isotropicand anisotropic Delaunay insertion...).FUNCTIONAL DESCRIPTION

The Mmg plateform gathers open source software for two-dimensional, surface and volume remeshing. Itprovides three applications : 1) mmg2d: generation of a triangular mesh , adaptation and optimization of atriangular mesh 2) mmgs: adaptation and optimization of a surface triangulation representing a piecewise linearapproximation of an underlying surface geometry 3) mmg3d: adaptation and optimization of a tetrahedralmesh and isovalue discretization

The platform software perform local mesh modifications. The mesh is iteratively modified until the userprescription satisfaction.

5.8. NOMESH• Participants: Cécile Dobrzynski and Algiane Froehly

• Partners: CNRS - IPB - Université de Bordeaux


KEYWORDS: Mesh - Curved mesh - Tetrahedral meshFUNCTIONAL DESCRIPTION

NOMESH is a software allowing the generation of three order curved simplicial meshes. Starting from a"classical" mesh with straight elements composed by triangles and/or tetrahedra, we are able to curve theboundary mesh. Starting from a mesh with some curved elements, we can verify if the mesh is valid, thatmeans there is no crossing elements and only positive Jacobian. If the curved mesh is non valid, we modify itusing linear elasticity equations until having a valid curved mesh.

http://www.mmgtools.org


5.9. SLOWSKEYWORDS: Free surface flows, Unstructured meshes, shallow water equations, Boussinesq equations

• Participants: Luca Arpaia, Andrea Filippini, Maria Kazolea, Mario Ricchiuto and Nikolaos Pattakos• Contact: Mario Ricchiuto


SLOWS (Shallow-water fLOWS) is a C-platform allowing the simulation of free surface shallow water flowswith friction. It can be used to simulate near shore hydrodynamics, wave transformations processes, etc. Thekernel of the CODE is a shallow water solver based on second order residual distribution or second and thirdorder finite volume schemes. Three different approaches are available to march in time, based on conditionallydepth-positivity preserving implicit schemes, or on conditionally depth-positivity preserving genuinely explicitdiscretizations, or on an unconditionally depth-positivity preserving space-time approach. Newton and frozenNewton loops are used to solve the implicit nonlinear equations. Linear algebraic sparse systems arising in thediscretization are solved with This year several enhancements have been implemented

• a correction of both the residual distribution and finite volume methods to solve the shallow waterequations in spherical (or Mercator) curvilinear coordinates;

• mass-conserving mesh movement to adapt an initial grid to wet-dry interfaces as well as to otherphysical features of the flow;

• a new library has been developed to enhance the shallow water equations. This library computesan algebraic source term by inverting an elliptic (grad-div type) PDE. The addition of this termto the shallow water version of SLOWS allows to recover the a fully nonlinear weakly dispersiveGreen-Naghdi solver. The solution of the elliptic PDE is performed with a classical Galerkin FEMapproach, and MUMPS is the MUMPS library is used to invert the resulting matrix;

• Initial optimization and OpenMP parallelization of the shallow water kernel.

SLOWS is our main simulation tool in both the TANDEM and Tides projects.

5.10. Sparse-PDDAdaptive sparse polynomial dimensional decomposition for global sensitivity analysisKEYWORDS: Stochastic models - Uncertainty quantification

• Participants: Pietro-Marco Congedo• Contact: Pietro-Marco Congedo


The polynomial dimensional decomposition (PDD) is employed in this code for the global sensitivity analysisand uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of inputrandom variables. Due to the intimate structure between the PDD and the Analysis of Variance (ANOVA)approach, PDD is able to provide a simpler and more direct evaluation of the Sobol sensitivity indices,when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms growsexponentially with respect to the size of the input random vector, which makes the computational cost ofstandard methods unaffordable for real engineering applications. In order to address the problem of the curseof dimensionality, this code proposes essentially variance-based adaptive strategies aiming to build a cheapmeta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed byregression. Three levels of adaptivity are carried out in this code: 1) the truncated dimensionality for ANOVAcomponent functions, 2) the active dimension technique especially for second- and higher-order parameterinteractions, and 3) the stepwise regression approach designed to retain only the most influential polynomialsin the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate modelrepresentation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-square regression problem is negligible. The size of the finally obtained sparse PDD representation is muchsmaller than the one of the full expansion, since only significant terms are eventually retained. Consequently,a much less number of calls to the deterministic model is required to compute the final PDD coefficients.



This code allows an efficient meta-modeling for a complex numerical system featuring a moderate-to-largenumber of uncertain parameters. This innovative approach involves polynomial representations combined withthe Analysis of Variance decomposition, with the objective to quantify the numerical output uncertainty andits sensitivity upon the variability of input parameters.

5.11. TUCWaveKEYWORDS: fre surface flows, Boussinesq equaions, weakly nonlinear models, unstructured grids

• Participants: Maria Kazolea, Argiris Delis and Ioannis Nikolos• Contact: Maria Kazolea


Fortran Planform which accounts for the study of near shore processes. TUCWave uses a high-order well-balanced unstructured finite volume (FV) scheme on triangular meshes for modeling weakly nonlinear andweakly dispersive water waves over varying bathymetries, as described by the 2D depth-integrated extendedBoussinesq equations of Nwogu (1993), rewritten in conservation law form. The FV scheme numericallysolves the conservative form of the equations following the median dual node-centered approach, for boththe advective and dispersive part of the equations. The code developed follows an efficient edge basedstructured technique. For the advective fluxes, the scheme utilizes an approximate Riemann solver along witha well-balanced topography source term up-winding. Higher order accuracy in space and time is achievedthrough a MUSCL-type reconstruction technique and through a strong stability preserving explicit Runge-Kutta time stepping. Special attention is given to the accurate numerical treatment of moving wet/dry frontsand boundary conditions. Furthermore, the model is applied to several examples of wave propagation overvariable topographies and the computed solutions are compared to experimental data. TUCWave is used in theTANDEM project to provide reference solutions with a weakly nonlinear and dispersive model.

6. New Results6.1. High order discretizations on unstructured meshes

• Participants: Héloise Beaugendre, Cécile Dobrzynski, Léo Nouveau, Mario Ricchiuto, QuentinViville

• Corresponding member: Héloise Beaugendre

Our work on high order unstructured discretizations this year has pursued three main avenues:• We have extended the team’s previous work on the consistent residual based approximation of

viscous flow equations to the framework of Immersed Boundary Methods (IBM). This is anincreasingly popular approach in Computational Fluid Dynamics as it simplifies the mesh generationproblem. In our work, we consider a technique based on the addition of a penalty term to the Navier-Stokes equations to account for the wall boundary conditions. To adapt the residual distributionmethod method to the IBM, we developed a new formulation based on a Strang splitting appproach intime. This approach, couples in a fully consistent manner an implicit asymptoticly exact integrationprocedure of the penalization ODE, with the explicit residual distribution discretization for theNavier-Stokes equations, based on the method proposed in [122]. The ODE integrator provides anoperator which is exact up to orders η2, with η the penalty parameter assuming values of the orderof 10−10. To preserve the accuracy of the spatial discretization in the Navier-Stokes step, we haveintroduced, in vicinity of the penalised region, a modification of the solution gradient reconstructionrequired for the evaluation of the viscous fluxes. We have shown formally and numerically that theapproach proposed is second order accurate for smooth solutions, and shown its potential whencombined with unstructured mesh adaptation strategies w.r.t. the (implicitly described) solid walls[16]. This approach has been combined with r−adaptation techniques to account for moving bodiesand validated on simulations involving flapping wings, and computations of ices block trajectoriesin the framework of the STORM project [56], [46];


• Another research axis consists in proposing a novel approach that allows to use p-adaptation withcontinuous finite elements. Under certain conditions, primarily the use of a residual distributionscheme, it is possible to avoid the continuity constraint imposed to the approximate solution, whilestill retaining the advantages of a method using continuous finite elements. The theoretical material,the complete numerical method and practical results show as a proof of concept that p-adaptation ispossible with continuous finite elements. This year, we extended the p-adaptation method to Navier-Stokes equations and coupled it with immersed boundary method.

• We have studied the high order approximation of problems with dispersion and suggested a routeallowing to construct high order methods (up to order 4) allowing to obtain the same accuracy for thesolution, and for its first and second order derivatives. Initial validation for the approach proposedhas been shown for the time dependent KdV equations [14], [49].

6.2. High order mesh generation and mesh adaptation• Participants: Luca Arpaia , Cécile Dobrzynski, Ghina El Jannoun, Léo Nouveau, Mario Ricchiuto

• Corresponding member: Cécile Dobrzynski

This year several new algorithmic improvements have been obtained which will allow to enhance our meshingtools:

• We have enhanced our work on r-adaptation techniques for time dependent equations. These tech-niques are based on mesh deformations obtained by solving continuous differential equations for thelocal displacements. These equations are controlled by an error monitor. Several improvements havebeen made. We have studied in depth the formulation of the coupling of the mesh movement with theflow solver. We have found that for both finite volume and residual distribution methods, a couplingof mesh and solution evolution (by means of an ALE method) provides accuracy enhancements, andis to be preferred to a simpler adapt-project-evolve approach. The method has been fully tested intwo space dimensions and preliminary results have been performed in three dimensions. We haveapplied this technic to immersed boundary methods to compressible simulations. For problems withsource terms, and in particular problems admitting some important physical invariants as the shallowwater equations, we have solved the conflict between the conservation of either mass or the invari-ant, allowing for the conservation of both quantities up to machine accuracy. In parallel we haveproposed a modified formulation of an elasticity equation allowing to reduce the nonlinearity of themesh PDE to the force imposed in the right hand side. Initial validation has been shown in [56] andin the PhD of L. Nouveau ;

6.3. Uncertainty Quantification and robust design optimization• Participants: Andrea Cortesi , Pietro Marco Congedo, Nassim Razaaly, Sanson Francois

• Corresponding member: Pietro Marco Congedo

We have developed an efficient sparse polynomial decomposition for sensitivity analysis and for building asurrogate in a problems featuring a large number of parameters. The Polynomial Dimensional Decomposition(PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) ofstochastic systems subject to a moderate to large number of input random variables. Due to the intimateconnection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to providea simpler and more direct evaluation of the Sobol sensitivity indices, when compared to the PolynomialChaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the sizeof the input random vector, which makes the computational cost of standard methods unaffordable for realengineering applications. In order to address the problem of the curse of dimensionality, this work proposesessentially variance-based adaptive strategies aiming to build a cheap meta- model (i.e. surrogate model) byemploying the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivityare carried out : 1) the truncated dimensionality for ANOVA component functions, 2) the active dimensiontechnique especially for second- and higher-order parameter interactions, and 3) the stepwise regression


approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptiveprocedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, sothat the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. Thesize of the finally obtained sparse PDD representation is much smaller than the one of the full expansion,since only significant terms are eventually retained. Consequently, a much smaller number of calls to thedeterministic model is required to compute the final PDD coefficients.

Concerning sensitivity analysis, we illustrate how third and fourth-order moments, i.e. skewness and kurtosis,respectively, can be decomposed mimicking the ANOVA approach. It is also shown how this decompositionis correlated to a Polynomial Chaos (PC) expansion leading to a simple strategy to compute each term. Newsensitivity indices, based on the contribution to the skewness and kurtosis, are proposed. The outcome of theproposed analysis is depicted by considering several test functions. Moreover, the ranking of the sensitivityindices is shown to vary according to their statistics order. Furthermore, the problem of formulating a truncatedpolynomial representation of the original function is treated. Both the reduction of the number of dimensionsand the reduction of the order of interaction between parameters are considered. In both cases, the impacton the reduction is assessed in terms of statistics, namely the probability density function. Feasibility of theproposed analysis in a real-case is then demonstrated by presenting the sensitivity analysis of the performancesof a turbine cascade in an Organic Rankine Cycles (ORCs), in the presence of complex thermodynamic modelsand multiple sources of uncertainty.

Moreover, we have developed a new framework for performing robust design optimization. a strategy isdeveloped to deal with the error affecting the objective functions in uncertainty-based optimization. Werefer to the problems where the objective functions are the statistics of a quantity of interest computed byan uncertainty quantification technique that propagates some uncertainties of the input variables throughthe system under consideration. In real problems, the statistics are computed by a numerical method andtherefore they are affected by a certain level of error, depending on the chosen accuracy. The errors on theobjective function can be interpreted with the abstraction of a bounding box around the nominal estimationin the objective functions space. In addition, in some cases the uncertainty quantification methods providingthe objective functions also supply the possibility of adaptive refinement to reduce the error bounding box.The novel method relies on the exchange of information between the outer loop based on the optimizationalgorithm and the inner uncertainty quantification loop. In particular, in the inner uncertainty quantificationloop, a control is performed to decide whether a refinement of the bounding box for the current design isappropriate or not. In single-objective problems, the current bounding box is compared to the current optimaldesign. In multi-objective problems, the decision is based on the comparison of the error bounding box ofthe current design and the current Pareto front. With this strategy, fewer computations are made for clearlydominated solutions and an accurate estimate of the objective function is provided for the interesting, non-dominated solutions. The results presented in this work prove that the proposed method improves the efficiencyof the global loop, while preserving the accuracy of the final Pareto front.

Concerning semi-intrusive methods, a novel multiresolution framework, namely the Truncate and Encode(TE) approach is generalized and extended for taking into account uncertainty in partial differential equations(PDEs). Innovative ingredients are given by an algorithm permitting to recover the multiresolution represen-tation without requiring the fully resolved solution, the possibility to treat a whatever form of pdf and theuse of high-order (even non-linear, i.e. data-dependent) reconstruction in the stochastic space. Moreover, thespatial-TE method is introduced, which is a weakly intrusive scheme for uncertainty quantification (UQ), thatcouples the physical and stochastic spaces by minimizing the computational cost for PDEs. The proposedscheme is particularly attractive when treating moving discontinuities (such as shock waves in compressibleflows), even if they appear during the simulations as it is common in unsteady aerodynamics applications.The proposed method is very flexible since it can easily coupled with different deterministic schemes, evenwith high-resolution features. Flexibility and performances of the present method are demonstrated on vari-ous numerical test cases (algebraic functions and ordinary differential equations), including partial differentialequations, both linear and non-linear, in presence of randomness.


We applied a part of this method to a problem associated to the atmospheric reentry. In fact, an accuratedetermination of the catalytic property of thermal protection materials is crucial to design reusable atmosphericentry vehicles. This property is determined by combining experimental measurements and simulations ofthe reactive boundary layer near the material surface. The inductively-driven Plasmatron facility at the vonKarman Institute for Fluid Dynamics provides a test environment to analyze gas-surface interactions undereffective hypersonic conditions. In this study, we develop an uncertainty quantification methodology to rebuildvalues of the gas enthalpy and material catalytic property from Plasmatron experiments. A non-intrusivespectral projection method is coupled with an in-house boundary-layer solver, to propagate uncertainties andprovide error bars on the rebuilt gas enthalpy and material catalytic property, as well as to determine whichuncertainties have the largest contribution to the outputs of the experiments. We show that the uncertaintiescomputed with the methodology developed are significantly reduced compared to those determined using amore conservative engineering approach adopted in the analysis of previous experimental campaigns.

6.4. Modelling of free surface flows• Participants: Luca Arpaia , Stevan Bellec , Mathieu Collin , Sebastien De Brye , Andrea Filippini ,

Maria Kazolea, Luc Mieussens, and Mario Ricchiuto

• Corresponding member: Mario Ricchiuto

We have introduced a new systematic method to obtain discrete numerical models for incompressible free-surface flows. our approach allows to recover discrete asymptotic equations from a semi-discretized form(keeping the vertical z variable and time continuous) of the incompressible Euler equations with free surface.In particular, starting from a (continuous) Galerkin finite element discretization in the horizontal direction,we perform an asymptotic analysis of the resulting semi-discrete system. This has allowed to obtain newdiscrete equivalents of the Peregrine equations [5], as well as enhanced variants in the spirit of [115].This has been done in the PhD of S. Bellec. We have demonstrated that the resulting discrete equationspresent dispersion characteristics much improved w.r.t. those obtained by directly discretizing the asymptoticBoussinesq equations with continuous finite elements. This has been confirmed by numerical experimentson long wave propagation benchmarks. Concerning more classical continuous Boussinesq models, additionalwork has been done to characterize some of their exact solutions. This has provided some improved solutionsto benchmark our codes, as well as some additional knownledge on these models [4].This year we extended our work on fully non-linear weakly dispersive wave models in two dimensionalhorizontal coordinates. The proposed framework in [11], to approximate the so-called Green-Naghdi equationsis followed. The method proposed, while remaining unsplit in time, is based on a separation of the elliptic andhyperbolic components of the equations. This separation is designed to recover the standard shallow waterequations in the hyperbolic step, so that the method can be written as an algebraic correction to an existingshallow water code. More precisely, we re-write the standard form of the equations by splitting the originalsystem in its elliptic and hyperbolic parts, through the definition of a new variable, accounting for the dispersiveeffects and having the role of a non-hydrostatic pressure gradient in the shallow water equations. We considera two-step solution procedure. In the first step we compute a source term by inverting the elliptic coerciveoperator associated to the dispersive effects; then in a hyperbolic step we evolve the flow variables by usingthe non-linear shallow water equations, with all nonhydrostatic effects accounted by the source computed inthe elliptic phase. The advantages of this procedure are firstly that the GN equations are used for propagationand shoaling, while locally reverting to the non-linear shallow water equations to model energy dissipation inbreaking regions. Secondly and from the numerical point of view, this strategy allows each step to be solvedwith an appropriate numerical method on arbitrary unstructured meshes. We propose a hybrid finite element(FE) finite volume (FV) scheme, where the elliptic part of the system is discretized by means of the continuousGalerkin FE method and the hyperbolic part is discretized using a third-order node-centered finite volume (FV)technique. This work was a part of Andrea Filippini’s PhD and a research paper is under preparation.


We also continue our study on wave breaking techniques on unstructured meshes [55]. In particular, weevaluate the coupling of both a weakly and a fully non-linear Boussinesq system with a turbulence model.We reformulate an evolution model for the turbulent kinetic energy, initially proposed by Nwogu [115], andevaluate its capabilities to provide sufficient dissipation in breaking regions. We also compare this dissipationto the one introduced by the numerical discretization. A research paper on the topic, is under preparation.Further more we studied and tested the application and validation of TUCWave code on the transformationbreaking and run-up of irregular waves. Its is the first time that an unstructured high-resolution FV numericalsolver for the 2D extended BT equations of Nwogu is tested on the generation and propagation of irregularwaves. A research paper is under preparation.

The tools developed have been also used intensively in funded research programs. Within the TANDEMproject, several benchmarks relevant to tsunami modelling have been performed and several common publi-cations with the project partners are submitted and/or in preparation [54], [45]. We also our code SLOWS, tostudy the conditions for tidal bore formation in convergent alluvial estuaries [7]. A new set of dimensionlessparameters has been introduced to describe the problem, and the code SLOWS has been used to explore thespace of these parameters allowing to determine a critical curve allowing to characterize an estuary as "boreforming" or not. Surprising physical behaviours, in terms of dissipation and nonlinearity of the tides, havebeen highlighted.

Finally, in collaboration with F. Veron (University of Delaware at Newark, USA), L. Mieussens has developeda model to describe the effect of rain falling on water waves [20]. This model is based on a kinetic descriptionof rain droplets that is used to compute the induced pression on a water wave. This allows to estimate thedissipation (or amplification) of the wave due to rainy conditions.

6.5. Wave energy conversion hydrodynamics• Participants: Umberto Bosi, Mario Ricchiuto• Corresponding member: Mario Ricchiuto

We have developed a prototype spectral element solver four a coupled set of differential equations modellingwave propagation (so-called outer domain), and the submerged flow under a floating body (inner domain). Bothsystems of equations are depth-averaged (Boussinesq type) systems involving some dispersive terms. They arefurther coupled to a force balance providing a (system of) ODE(s) for the floater. This model constitutes anintermediate fidelity approximation for the hydrodynamics of a wave energy converter. Differently from allindustrial state of the art, it is a (fully) nonlinear model. However, its cost is extremely low when comparedto full three-dimensional CFD analyses, due to the dimensional reduction brought from the depth averagedmodelling. Last year we have shown the potential of this approach to predict the hydrodynamics of a floaterin a simplified case [90], [91] (journal version to appear on J. Ocean Eng. and Marine Energy). This year wehave further studied the issue of the coupling between domains with different PDE models (as in our casethe inner and outer domains), and suggested an approach (based on a first order reformulation) allowing tocoupled domains with different equations and with or without dispersive effects on either side. This work isdone in the framework of the MIDWEST project funded by the EU OCEANEranet call.

7. Bilateral Contracts and Grants with Industry7.1. Bilateral Contracts with Industry

Several contracts have been realized:• SAFRAN-HERAKLES, 20Keuros for the development of a code for computing low-probability.• CNES, 10 KEuros, for the technological transfer of Sparse-PDD code.• CEA 2015 10237, 60 Keuro for the supervision of the post-doc of Maxence Clayes by P.M. Congedo• CEA 16-CIFRE PELUCHON, 20 Keuro for the supervision by L. Mieussens of the PhD of Simon

Peluchon at the CEA-CESTA (1/1/15 - 31/12/17)• BGS IT&E (2016-2018), 20 Keuro for a consulting by M. Ricchiuto on the implantation of some of

the technology in the code SLOWS in their in-house model.


8. Partnerships and Cooperations

8.1. Regional InitiativesCRA 15/ THESE SANSON 10199These co-funded by Airbus Safran Launchers and the Aquitaine Region during the period 2016-2019Topic : uncertainty propagation approach in a system of codesVIPER ProjetThese co-funded by the Aquitaine Region and Inria. PhD student to recruit during the period 2017-2020Topic : robust design of the EVE engine in collaboration with the SME EXOES.Title: TIDES: Robust simulation tools for non-hydrostatic free surface flowsType: Apple à Projets Recherche du Conseil de la Région AquitaineCoordinator: M. RicchiutoOther partners: UMR EPOC (P. Bonneton)Abstract: This project proposes to combine modern high order adaptive finite elements techniqueswith state of the art nonlinear and non-hydrostatic models for free surface waves to provide anaccurate tool for the simulation of near shore hydrodynamics, with application to the study andprediction of tidal bores. The Garonne river will be used as a case study. This project co-funds(50%) the PhD of A. Filippini.

8.2. National Initiatives8.2.1. ANR MAIDESC

Title: Maillages adaptatifs pour les interfaces instationnaires avec deformations, etirements, courbu-res.Type: ANRDuration: 48 monthsStarting date : 1st Oct 2013Coordinator: Dervieux Alain (Inria Sophia)Abstract: Mesh adaptive numerical methods allow computations which are otherwise impossible dueto the computational resources required. We address in the proposed research several well identifiedmain obstacles in order to maintain a high-order convergence for unsteady Computational Mechanicsinvolving moving interfaces separating and coupling continuous media. A priori and a posteriorierror analysis of Partial Differential Equations on static and moving meshes will be developedfrom interpolation error, goal-oriented error, and norm-oriented error. From the minimization ofthe chosen error, an optimal unsteady metric is defined. The optimal metric is then converted into asequence of anisotropic unstructured adapted meshes by means of mesh regeneration, deformation,high stretching, and curvature. A particular effort will be devoted to build an accurate representationof physical phenomena involving curved boundaries and interfaces. In association with curvedboundaries, a part of studies will address third-order accurate mesh adaption. Mesh optimalityproduces a nonlinear system coupling the physical fields (velocities, etc.) and the geometrical ones(unsteady metric, including mesh motion). Parallel solution algorithms for the implicit coupling ofthese different fields will be developed. Addressing efficiently these issues is a compulsory conditionfor the simulation of a number of challenging physical phenomena related to industrial unsolved orinsufficiently solved problems. Non-trivial benchmark tests will be shared by consortium partnersand by external attendees to workshops organized by the consortium. The various advances will beused by SME partners and proposed in software market.


8.2.2. PIA TANDEMTitle: Tsunamis in the Atlantic and the English ChaNnel: Definition of the Effects through numericalModeling (TANDEM)Type: PIA - RSNR (Investissement d’Avenir, “Recherches en matière de Sûreté Nucléaire etRadioprotection”)Duration: 48 monthsStarting date : 1st Jan 2014Coordinator: H. Hebert (CEA)Abstract: TANDEM is a project dedicated to the appraisal of coastal effects due to tsunami waveson the French coastlines, with a special focus on the Atlantic and Channel coastlines, where Frenchcivil nuclear facilities have been operated since about 30 years. As identified in the call RSNR, thisproject aims at drawing conclusions from the 2011 catastrophic tsunami, in the sense that it willallow, together with a Japanese research partner, to design, adapt and check numerical methods oftsunami hazard assessment, against the outstanding observation database of the 2011 tsunami. Thenthese validated methods will be applied to define, as accurately as possible, the tsunami hazard forthe French Atlantic and Channel coastlines, in order to provide guidance for risk assessment on thenuclear facilities.

8.2.3. APP Bordeaux 1Title : Reactive fluid flows with interface : macroscopic models and application to self-healingmaterialsType : Project Bordeaux 1Duration : 36 monthsStarting : September 2014Coordinator : M. ColinAbstract : Because of their high strength and low weight, ceramic-matrix composite materials(CMCs) are the focus of active research, for aerospace and energy applications involving hightemperatures. Though based on brittle ceramic components, these composites are not brittle dueto the use of a fiber/matrix interphase that manages to preserve the fibers from cracks appearingin the matrix. The lifetime-determining part of the material is the fibers, which are sensitive tooxidation; when the composite is in use, it contains cracks that provide a path for oxidation. Theobtained lifetimes can be of the order of hundreds of thousands of hours. These time spans makemost experimental investigations impractical. In this direction, the aim of this project is to furnishpredictions based on computer models that have to take into account: 1) the multidimensionaltopology of the composite made up of a woven ceramic fabric; 2) the complex chemistry takingplace in the material cracks; 3) the flow of the healing oxide in the material cracks.

8.2.4. APP University of BordeauxTitle : Modélisation d’un système de dégivrage thermiqueType : Project University of BordeauxDuration : 36 monthsStarting : October 2016Coordinator : H. Beaugendre and M. ColinAbstract : From the beginning of aeronautics, icing has been classified as a serious issue : iceaccretion on airplanes is due to the presence of supercooled droplets inside clouds and can lead tomajor risks such as aircrash for example. As a consequence, each airplane has its own protectionsystem : the most important one is an anti-icing system which runs permanently. In order toreduce gas consumption, de-icing systems are developed by manufacturers. One alternative to real


experiment consists in developing robust and reliable numerical models : this is the aim of thisproject. These new models have to take into account multi-physics and multi-scale environnement :phase change, thermal transfer, aerodynamics flows, etc. We aim to use thin films equations coupledto level-set methods in order to describe the phase change of water. The overall objective is to providea simulation plateform, able to provide a complete design of these systems.

8.3. European Initiatives8.3.1. FP7 & H2020 Projects8.3.1.1. UTOPIA

Type: COOPERATION

Instrument: Specific Targeted Research Project

Objectif: The main objectives of this research programme are to develop, through the ESR’s in-dividual projects, fundamental mathematical methods and algorithms to bridge the gap betweenUncertainty Quantification and Optimisation and between Probability Theory and Imprecise Prob-ability Theory for Uncertainty Quantification, and to efficiently solve high-dimensional, expensiveand complex engineering problems.

Duration: 2017 - 2021

Coordinator: University of Strathclyde (Scotland, UK)

Partner: University of Strathclyde (Scotland, UK), Inria Bordeaux Sud-Ouest (France), ESTECO(Italy), CIRA, Centro Italiano Aerospaziali (Italy), Politecnico di Milano (Italy), Jozef StefanInstitute (Slovenia), Cologne University of Applied Sciences (Germany), University of Durham(England, UK), Ghent University (Belgium), Von Karman Institute (Belgium), DLR, Institute ofAerodynamics and Flow Technology (Germany), National Physical Laboratory (England, UK),Leonardo Aircraft S.p.A (Italy), Airbus Operations Gmbh (England, UK), Stanford University(USA)

Inria contact: Pietro Marco Congedo

Abstract: Research activities will be developed in the context of the European project - UTOPIAEhttp://utopiae.eu (520 K euros for Inria). The aim of this project is to develop, through the ESRsindividual projects, fundamental mathematical methods and algorithms to efficiently solve high-dimensional, expensive and complex engineering problems. Two PhD thesis will be recruited at thebeginning of 2017.

8.3.1.2. STORM

Type: COOPERATION

Instrument: Specific Targeted Research Project

Duration: October 2013 - September 2016

Coordinator: SNECMA (France)

Partner: SNECMA SA (FR), AEROTEX UK LLP (UK), AIRBUS OPERATIONS SL (ES),Airbus Operations Limites (UK), AIRCELLE SA (FR), ARTTIC (FR), CENTRO ITALIANORICERCHE AEROSPAZIALI SCPA (IT), CRANFIELD UNIVERSITY (UK), DEUTSCHES ZEN-TRUM FUER LUFT - UND RAUMFAHRT EV (DE), EADS DEUTSCHLAND GMBH (DE), ON-ERA (FR), TECHSAPACE AERO SA (BE)

Inria contact: Héloise Beaugendre

http://utopiae.eu


Abstract: During the different phases of a flight, aircraft face severe icing conditions. When thisice then breaks away, and is ingested through the reminder of the engine and nacelle it createsmultiple damages which have a serious negative impact on the operations costs and may alsogenerate some incident issues. To minimise ice accretion, propulsion systems (engine and nacelle)are equipped with Ice Protection Systems (IPS), which however have themselves performance issues.Design methodologies used to characterise icing conditions are based on empirical methods andpast experience. Cautious design margins are used non-optimised designs solutions. In addition,engine and nacelle manufacturers are now limited in their future architectures solutions developmentbecause of lack of knowledge of icing behaviour within the next generation of propulsive systemssolutions, and of new regulations adopted that require aero engine manufacturers to address anextended range of icing conditions.

In this context that STORM proposes to: characterise ice accretion and release through partialtests ; Model ice accretion, ice release and ice trajectories ; Develop validated tools for runback ;characterise ice phobic coatings ; select and develop innovative low cost and low energy anti-icingand de-icing systems. Thus, STORM will strengthen the predictability of the industrial design toolsand reduce the number of tests needed. It will permit lower design margins of aircraft systems, andthus reduce the energy consumption as well as prevent incidents and break downs due to icing issues.

8.3.2. Collaborations in European Programs, Except FP7 & H2020Program: OCEANEraNET

Project acronym: MIDWEST

Project title: Multi-fIdelity Decision making tools for Wave Energy SysTems

Duration: December 2015 - December 2018

Coordinator: Mario Ricchiuto

Other partners: Chalmers University (Sweden), DTU Compute (Denmark), IST Lisbon (Portugal)

Abstract: Wave energy converters (WECs) design currently relies on low-fidelity linear hydrody-namic models. While these models disregard fundamental nonlinear and viscous effects - whichmight lead provide sub-optimal designs - high-fidelity fully nonlinear Navier-Stokes models are pro-hibitively computational expensive for optimization. The MIDWEST project will provide an efficientasymptotic nonlinear finite element model of intermediate fidelity, investigate the required fidelitylevel to resolve a given engineering output, construct a multi-fidelity optimization platform usingsurrogate models blending different fidelity models. Combining know how in wave energy technol-ogy, finite element modelling, high performance computing, and robust optimization, the MIDWESTproject will provide a new efficient decision making framework for the design of the next generationWECs which will benefit all industrial actors of the European wave energy sector.

8.4. International Initiatives8.4.1. Inria International Labs

Inria@SiliconValleyAssociate Team involved in the International Lab:

8.4.1.1. AQUARIUS2

Title: Advanced methods for uncertainty quantification in compressible flows

International Partner (Institution - Laboratory - Researcher):

Stanford (United States) - Department of Mechanical Engineering - Gianluca Iaccarino

Start year: 2014

See also: http://www.stanford.edu/group/uq/aquarius/index3.html

http://www.stanford.edu/group/uq/aquarius/index3.html


This research project deals with uncertainty quantification in computational fluid dynamics. Un-certainty Quantification (UQ) aims at developing rigorous methods to characterize the impact oflimited knowledge on quantities of interest. Main objective of this collaboration is to build a flexibleand efficient numerical platform, using intrusive methods, for solving stochastic partial differentialequations. In particular, the idea is to handle highly non-linear system responses driven by shocks.

8.4.1.2. AMoSS

Title: Advanced Modeling on Shear Shallow Flows for Curved Topography : water and granularflows.

International Partner (Institution - Laboratory - Researcher):

Inria Sophia-Antipolis and University of Nice (France)

Inria Bordeaux and University of Bordeaux (France)

University of Marseille (France)

National Cheng Kung University, Tainan, Taiwan

National Taiwan University and Academia Sinica,Taipei, Taiwan

Duration: 2014 - 2016

See also: https://team.inria.fr/amoss/

Our objective is to generalize the promising modeling strategy proposed in G.L. Richard and S.L.Gavrilyuk 2012, to genuinely 3D shear flows and also take into account the curvature effects relatedto topography. Special care will be exercised to ensure that the numerical methodology can takefull advantage of massively parallel computational platforms and serve as a practical engineeringtool. At first we will consider quasi-2D sheared flows on a curve topography defined by an arc,such as to derive a model parameterized by the local curvature and the nonlinear profile of the bed.Experimental measurements and numerical simulations will be used to validate and improve theproposed modeling on curved topography for quasi-2D flows. Thereafter, we will focus on 3D flowsfirst on simple geometries (inclined plane) before an extension to quadric surfaces and thus preparethe generalization of complex topography in the context of geophysical flows.

8.4.1.3. Informal International Partners

University of Zurich : R. Abgrall. Collaboration on penalisation on unstructured grids and high orderadaptive methods for CFD and uncertainty quantification.

Politecnico di Milano, Aerospace Department (Italy) : Pr. A. Guardone. Collaboration on ALE forcomplex flows (compressible flows with complex equations of state, free surface flows with movingshorelines).

von Karman Institute for Fluid Dynamics (Belgium). With Pr. T. Magin we work on UncertaintyQuantification problems for the identification of inflow condition of hypersonic nozzle flows. WithPr. H. Deconinck we work on the design of high order methods, including goal oriented meshadaptation strategies

NASA Langley: Dr. Alireza Mazaheri. Collaboration on high order schemes for PDEs with secondand third order derivatives, with particular emphasis on high order approximations of solutionderivatives.

Technical University of Crete, School of Production Engineering & Management : Pr. A.I. Delis.Collaboration on high order schemes for depth averaged free surface flow models, including robustcode to code validation

Chalmers University (C. Eskilsson) and Technical University of Denmark (A.-P. Engsig-Karup) :our collaboration with Chalmers and with DTU compute in Denmark aims at developing highorder non hydrostatic finite element Boussinesq type models for the simulation floating wave energyconversion devices such as floating point absorbers ;

https://team.inria.fr/amoss/


University of Delaware: F. Veron. Collaboration on the modelling of rain effects on wave propaga-tion.

8.5. International Research Visitors8.5.1. Visits of International Scientists

• From 27/11 to 03/12/2016 Pascal POULLET (Université des Antilles) has visited M. Ricchiuto towork on nonlinear residual based approximations of free sudface flows with moving bathymetries.

• From 21/11 to 09/12/2016 Luca CIRROTTOLA (Politecnico di Milano) has visited C. Dobrizinskyto work on parallel mesh adaptation.

• From 21/10 to 05/11/2016 François MORENCY (ETS, University of Québec, Montréal) has visitedus to work on LESCAPE code with Héloïse, Léo and Aurore. The Spalart-Allmaras turbulent modelhas been validated using the perodic channel flow test case.

• From 01/10 to 29/10/2016 Claes ESKILSSON (Chalmers University of Technology, Sweden) hasvisited us to work with Mario Ricchiuto and U. Bosi on spectral element methods for Boussinesqmodels with floating structures.

• From 12/09 to 22/09/2016 Kazuo AOKI (University of Taiwan) has visited us to work with LucMieussens on models for reentry flows.

• From 07/07 to 09/07/2016 Volker ROEBER (Tohoku University, International Research Institute ofDisaster Science) has visited us to work with Maria Kazolea and Mario Ricchiuto on robust code tocode validation, on coastal engineering problems.

• From 27/03 to 01/04/2016 Alireza MAZAHERI (NASA Langley) came to visit Mario Ricchiuto andV. Perrier to work on the implementation of a hyperbolic formulation of the Navier-Stokes equationsin the AeroSol platform.

• From 16/03/2016 Guglielmo SCOVAZZI (Duke University) has visited M. Ricchiuto to work onstabilized finite elements for geo-mechanics.

• From 1/01/2016 to 31/04/2016 Gianluca IACCARINO (Stanford University) has visited the Teamin the context of AQUARIUS Team, collaborating actively with all the PhD student involved inuncertainty quantification research. All the students involved (Razaaly, Sanson and Cortesi) havethen visited the group of G. Iaccarino in Stanford University in the fall 2016.

• From 15/05/2016 to 17/07/2016 Fabrice VERON (University of Delaware at Newark, USA) hasvisited us to work with Luc Mieussens on a project dedicated to the modelling and simulation of theinteraction rain/water waves.

• From April 2015 to April 2016 : T. WATANABE, Department of Mathematics, Faculty of ScienceKyoto Sangyo University visited M. Colin to work on the approximation of solitary wave solutionsof nonlinear dispersive PDEs.

8.5.1.1. Internships• From Feb 2016 to Jul 2016 Rama Ayoub (Inria, M. Sc. Student)• From Apr 2016 to Sep 2016 Toufik Boubehziz (EDF, M. Sc. Student )• From Jan 2016 to Mar 2016 Maxence Claeys (CEA, Phd Student)• From Feb 2016 to Jul 2016 Antoine Fondaneche (Inria, M. Sc. Student)• From Oct 2016 to Feb 2016 Esben Grange (Inria, M. Sc. Student)• From Jun 2016 to Sep 2016 Adrien Paumelle (Inria, Univ. Bordeaux )• From May 2016 to Sep 2016 Raphael Robyn (Inria, Univ. Bordeaux)

9. Dissemination9.1. Promoting Scientific Activities9.1.1. Scientific Events Organisation9.1.1.1. Member of the Organizing Committees

H. Beaugendre: Numerical workshop for the STORM European project, Inria Bordeaux, France, November2016


M. Colin: Congress JEF, dedicated to young researchers in PDE analysis and applications, Bordeaux, France,March 2016M. Ricchiuto : International workshop B’WAVES 2016, Bergen, Norway, June 2016 ( https://project.inria.fr/tsunamischool2016/)M. Ricchiuto : TANDEM and Defis Littoral Tsunami School, Bordeaux, France, April 2016 (http://www.uib.no/en/bwaves2016)M. Ricchiuto : Verification, Validation et Quantification des incertitudes en simulation numerique (VVUQ),Aristote seminar cycles, Ecole Polytechnique, France, November 2016 (http://www.association-aristote.fr/doku.php/association-aristote.fr_doku.php_simulation)

9.1.2. Scientific Events Selection9.1.2.1. Member of the Conference Program Committees

P.M. Congedo : NICFD 2016 Conference, Varenna, Italy, October 2016.

9.1.3. Journal9.1.3.1. Member of the Editorial Boards

Mathieu Colin is a member of the board of the journal Applications and Applied Mathematics: An Interna-tional Journal (AAM)Mario Ricchiuto is member of the editorial board of Computers & Fluids (Elsevier), and of GEM - Interna-tional Journal on Geomathematics (Springer)A special issue of the European Journal of Mechanics / B Fluids will be dedicated to the 2 editions of theinternational workshop B’Waves on wave breaking, held in 2014 in Bordeaux (M. Colin and M. Ricchiutoas co-organizers), and in 2016 in Bergen (M. Ricchiuto as co-organizer). M. Colin and M. Ricchiuto will beguest editors of this issue

9.1.3.2. Reviewer - Reviewing Activities

We reviewed papers for top international journals in the main scientific themes of the team : journal of Compu-tational Physics, Computer Methods in Applied Mechanics and Engineering, Optimization and Engineering,International Journal of Numerical Methods in Fluids, Physics of Fluids, Journal of Marine Science and Tech-nology, Engineering Applications of Computational Fluid Mechanics, Computers and Fluids, InternationalJournal of Modelling and Simulation in Engineering Aircraft Engineering and Aerospace Technology, Inter-national Journal of Computational Fluid Dynamics, Applications and applied mathematics : An internationaljournal, Discrete and Continuous Dynamical Systems - Series A, Electronic Journal of Differential Equa-tions, Calculus of Variations and Partial Differential Equations, Nonlinear Analysis: Modelling and Control,Advanced Nonlinear Studies, Communications on Pure and Applied Analysis, Communications in Compu-tational Physics, Nonlinearity, Applications and Applied Mathematics: An International Journal, Journal ofDifferential Equations, Analysis and Mathematical Physics.

9.1.4. Invited Talks• P.M. Congedo, Presentation at Journees Scientifiques Inria, June 2016, Rennes

• P.M. Congedo, “General introduction to Uncertainty Quantification”, CNES, March 2016, Toulouse

• M. Kazolea, “Wave breaking in Boussinesq free sruface models”, International WorkshopB’Waves2016, Bergen (Norway)

• M. Ricchiuto, “Numerical issues in tsunami simulation: dispersion and diffusion ?scales?, what orderof accuracy ?”, TANDEM and Defis Littoral 2016 Tsunami school, Bordeaux

9.1.5. Leadership within the Scientific CommunityP.M. Congedo has been appointed as the Co-Director of the Inria International Lab Inria-CWI.

https://project.inria.fr/tsunamischool2016/

https://project.inria.fr/tsunamischool2016/

http://www.uib.no/en/bwaves2016

http://www.uib.no/en/bwaves2016

http://www.association-aristote.fr/doku.php/association-aristote.fr_doku.php_simulation

http://www.association-aristote.fr/doku.php/association-aristote.fr_doku.php_simulation


9.2. Teaching - Supervision - Juries9.2.1. Teaching

Licence : Cécile Dobrzynski, Langages en Fortran 90, 54h, L3, ENSEIRB-MATMÉCA, FRANCEMaster : Héloïse Beaugendre, TP langage C++, 48h, M1, ENSEIRB-MATMÉCA, FRANCEMaster : Héloïse Beaugendre, Calcul Haute Performance (OpenMP-MPI), 40h, M1, ENSEIRB-MATMÉCA et Université de Bordeaux, FranceMaster : Héloïse Beaugendre, Initiation librairie MPI, 12h, M2, Ecole de Technologie Superieure,Université du Québec, Montréal, CanadaMaster : Héloïse Beaugendre, Responsable de filière de 3ème année, 15h, M2, ENSEIRB-MATMÉCA, FranceMaster : Héloïse Beaugendre, Calcul parallèle (MPI), 78h, M2, ENSEIRB-MATMÉCA, FranceMaster : Héloïse Beaugendre, Encadrement de projets de la filière Calcul Haute Performance, 11h,M2, ENSEIRB-MATMÉCA, FranceMaster : Héloïse Beaugendre , Projet fin d’études, 4h, M2, ENSEIRB-MATMÉCA, FRANCEMaster : Mathieu Colin : Integration, M1, 54h, ENSEIRB-MATMÉCA, FRANCEMaster : Mathieu Colin : PDE, M2, 30h, ENSEIRB-MATMÉCA, FRANCEMaster : Mathieu Colin : Fortran 90, M1, 44h, ENSEIRB-MATMÉCA, FRANCEMaster : Mathieu Colin : PDE, M1, 28h, University of Bordeaux, FRANCEMaster : Mathieu Colin : Analysis, L1, 47h, ENSEIRB-MATMÉCA, FRANCEMaster: Luc Mieussens, Transport de particules : modèles, simulation, et applications, 24h, M2,ENSEIRB-MATMECA, FranceMaster : Luc Mieussens, Projet fin d’études, 4h, M2, ENSEIRB-MATMÉCA, FRANCEDoctorat : P.M. Congedo, Uncertainty quantification, theory and application to algorithms, CFD andglobal change, Apr 2015, CERFACS, Toulouse, France, 4h.Master : Mario Ricchiuto : Fluid Dynamics II, 20h, ENSEIRB-MATMÉCA, FRANCEMaster : Mario Ricchiuto, Encadrement de projets TER, 10h, ENSEIRB-MATMÉCA, FRANCE

9.2.2. SupervisionHdR : Héloise Beaugendre, Contributions à la simulation numérique des écoulements fluides :exemples en milieu poreux et en aéronautique , Bordeaux University, 18 March 2016.PhD : Fusi Francesca, Stochastic robust optimization of a helicopter rotor airfoil, March 2016.PhD : Bellec Stevan, Discrete asymptotic modelling of free surface flows, 5 October 2016.PhD : Viville Quentin, Construction d’une méthode hp-adaptative pour les schémas aux RésidusDistribués, Bordeaux University, 22 November 2016.PhD: Filippini Andrea, Nonlinear finite element Boussinesq modelling of non-hydrostatic freesurface flows, 14 December 2016.PhD: Nouveau Léo, Adaptative Residual Based Schemes for Solving the Penalized Navier-StokesEquations with Moving Bodies - Application to Ice Shedding Trajectories, Bordeaux University, 16December 2016.PhD in progress : Arpaia Luca, Continuous mesh deformation and coupling with uncertaintyquantification for coastal inundation problems, started in March 2014.PhD in progress : Bosi, Umberto, ALE spectral element Boussinesq modelling of wave energyconverters, started in November 2015PhD in progress : Cortesi Andrea, Predictive numerical simulation for rebuilding freestream condi-tions in atmospheric entry flows, started in October 2014.


PhD in progress: Lin Xi, Asymptotic modelling of incompressible reactive flows in self-healingcomposites, started in October 2014.PhD in progress: Perrot Gregory, Physico-chemical modelling of self-healing ceramic composites,started in October 2011.PhD in progress : Peluchon Simon, Approximation numérique et modélisation de l’ablation différen-tielle de deux matériaux: application à l’ablation liquide. Started in December 2014. Advisor: LucMieussens. PhD hosted in CEA-CESTA.PhD in progress: Aurore Fallourd, Modeling and Simulation of inflight de-icing systems, Started inOctober 2016.PhD in progress: Guillaume Jeanmasson, Explicit methods with local time stepping for the sim-ulation of unsteady turbulent flows. Started in October 2016. Advisor: Luc Mieussens. Hosted inONERA Châtillon.PhD in progress: Francois Sanson, Uncertainty propagation in a system of codes, started in February2016.PhD in progress: Nassim Razaaly, Robust optimization of ORC systems, started in February 2016.

9.2.3. JuriesP.M. Congedo : Rapporteur de thèse de Elio Bufi, ENSAM Paris Tech, December 2016.

10. BibliographyPublications of the year

Doctoral Dissertations and Habilitation Theses

[1] H. BEAUGENDRE. Contributions à la simulation numérique des écoulements fluides : exemples en milieuporeux et en aéronautique, Université de Bordeaux, March 2016, Habilitation à diriger des recherches, https://hal.inria.fr/tel-01315897

Articles in International Peer-Reviewed Journals

[2] R. ABGRALL, H. ALCIN, H. BEAUGENDRE, C. DOBRZYNSKI, L. NOUVEAU. Residual Schemes Applied toan Embedded Method Expressed on Unstructured Adapted Grids, in "Acta Aerodynamica Sinica", 2016, vol.34, no 2, pp. 214-223 [DOI : 10.7638/KQDLXXB-2016.0010], https://hal.inria.fr/hal-01407945

[3] R. ABGRALL, P. M. CONGEDO, G. GERACI. Towards a unified multiresolution scheme for treating disconti-nuities in differential equations with uncertainties, in "Mathematics and Computers in Simulation", February2016, https://hal.inria.fr/hal-01267140

[4] S. BELLEC, M. COLIN. On the existence of solitary waves for Boussinesq type equations and a newconservative model, in "Advances in Differential Equations", 2016, vol. 21, no 9,10, pp. 945-976, https://hal.inria.fr/hal-01378585

[5] S. BELLEC, M. COLIN, M. RICCHIUTO. Discrete asymptotic equations for long wave propagation, in "SIAMJournal on Numerical Analysis", 2016, https://hal.inria.fr/hal-01378612

[6] P. BENARD, G. BALARAC, V. MOUREAU, C. DOBRZYNSKI, G. LARTIGUE, Y. D’ANGELO. Mesh adaptationfor large-eddy simulations in complex geometries, in "International Journal for Numerical Methods in Fluids",2016 [DOI : 10.1002/FLD.4204], https://hal.archives-ouvertes.fr/hal-01339519

https://hal.inria.fr/tel-01315897

https://hal.inria.fr/tel-01315897

https://hal.inria.fr/hal-01407945





https://hal.archives-ouvertes.fr/hal-01339519


[7] P. BONNETON, A. G. FILIPPINI, L. ARPAIA, N. BONNETON, M. RICCHIUTO. Conditions for tidal boreformation in convergent alluvial estuaries, in "Estuarine, Coastal and Shelf Science", 2016, vol. 172, pp. 121- 127 [DOI : 10.1016/J.ECSS.2016.01.019], https://hal.inria.fr/hal-01266428

[8] M. COLIN, L. DI MENZA, J.-C. SAUT. Solitons in quadratic media, in "Nonlinearity", 2016, vol. 29, no 3,pp. 1000-1035, https://hal.inria.fr/hal-01254663

[9] M. COLIN, T. WATANABE. Cauchy problem for the nonlinear Klein-Gordon equation coupled with theMaxwell equation, in "Journal of Mathematical Analysis and Applications", 2016, vol. 443, no 2, pp. 778-796[DOI : 10.1016/J.JMAA.2016.05.057], https://hal.inria.fr/hal-01378608

[10] M. COLIN, T. WATANABE. On the existence of Ground states for a nonlinear Klein-Gordon-Maxwell typesystem, in "Funkcialaj ekvacioj.Serio internacia", 2016, https://hal.inria.fr/hal-01378611

[11] A. G. FILIPPINI, M. KAZOLEA, M. RICCHIUTO. A flexible genuinely nonlinear approach for non-linear wave propagation, breaking and runup, in "Journal of Computational Physics", 2016, vol. 310[DOI : 10.1016/J.JCP.2016.01.027], https://hal.inria.fr/hal-01266424

[12] F. FUSI, P. M. CONGEDO. An adaptive strategy on the error of the objective functions for uncertainty-basedderivative-free optimization, in "Journal of Computational Physics", February 2016, vol. 309, pp. 241–266[DOI : 10.1016/J.JCP.2016.01.004], https://hal.inria.fr/hal-01251604

[13] G. GERACI, P. M. CONGEDO, R. ABGRALL, G. IACCARINO. High-order statistics in global sensitivityanalysis: decomposition and model reduction, in "Computer Methods in Applied Mechanics and Engineering",January 2016, https://hal.inria.fr/hal-01247458

[14] A. MAZAHERI, M. RICCHIUTO, H. NISHIKAWA. A first-order hyperbolic system approach for dispersion,in "Journal of Computational Physics", 2016, vol. 321, pp. 593 - 605 [DOI : 10.1016/J.JCP.2016.06.001],https://hal.inria.fr/hal-01390677

[15] F. MORENCY, H. BEAUGENDRE. Mathematical model for ice wall interactions within a level set method, in"International Journal of Engineering Systems Modelling and Simulation", 2016, vol. 8, no 2, pp. 125-135,https://hal.inria.fr/hal-01250169

[16] L. NOUVEAU, H. BEAUGENDRE, C. DOBRZYNSKI, R. ABGRALL, M. RICCHIUTO. An adaptive, residualbased, splitting approach for the penalized Navier Stokes equations, in "Computer Methods in AppliedMechanics and Engineering", February 2016, vol. 303, pp. 208-230 [DOI : 10.1016/J.CMA.2016.01.009],https://hal.inria.fr/hal-01275807

[17] S. PAVAN, M. HERVOUET, M. RICCHIUTO, R. ATA. A second order residual based predictor–correctorapproach for time dependent pollutant transport, in "Journal of Computational Physics", 2016, vol. 318, pp.122 - 141 [DOI : 10.1016/J.JCP.2016.04.053], https://hal.inria.fr/hal-01308419

[18] F. SANSON, N. VILLEDIEU, F. PANERAI, O. CHAZOT, P. M. CONGEDO, T. E. MAGIN. Quantifi-cation of uncertainty on the catalytic property of reusable thermal protection materials from high en-thalpy experiments, in "Experimental Thermal and Fluid Science", January 2017, vol. 82, pp. 414-423[DOI : 10.1016/J.EXPTHERMFLUSCI.2016.11.013], https://hal.inria.fr/hal-01398173














[19] K. TANG, P. M. CONGEDO, R. ABGRALL. Adaptive surrogate modeling by ANOVA and sparse polynomialdimensional decomposition for global sensitivity analysis in fluid simulation, in "Journal of ComputationalPhysics", March 2016, https://hal.inria.fr/hal-01286721

[20] F. VERON, L. MIEUSSENS. A kinetic model for particle-surface interaction applied to rain falling on waterwaves, in "Journal of Fluid Mechanics", 2016, vol. 796, pp. 767-787 [DOI : 10.1017/JFM.2016.252], https://hal.archives-ouvertes.fr/hal-01245956

Invited Conferences

[21] H. BEAUGENDRE. Advanced numerical methods for ice trajectory calculations, in "MUSAF III", Toulouse,France, September 2016, https://hal.inria.fr/hal-01403248

[22] H. BEAUGENDRE. Numerical simulation of ice block trajectories, in "Conference LIAFSMA, Sino-FrenchConference on Applied Mathematics", Bordeaux, France, Bordeaux University, May 2016, https://hal.inria.fr/hal-01409292

[23] S. BRULL, L. FORESTIER-COSTE, L. MIEUSSENS. Local velocity grids for deterministic simulations ofrarefied flows, in "European Congress on Computational Methods in Applied Sciences and Engineering(ECCOMAS)", Crete, France, June 2016, https://hal.archives-ouvertes.fr/hal-01397475

[24] G. DECHRISTÉ, L. MIEUSSENS. Numerical Simulation of the Crookes Radiometer, in "Séminaire de Mé-canique des Fluides Numériques CEA-GAMNI", Paris, France, January 2016, https://hal.archives-ouvertes.fr/hal-01397477

International Conferences with Proceedings

[25] P. M. CONGEDO. General introduction to Uncertainty Quantification, in "CNES Meeting", Toulouse, France,March 2016, https://hal.inria.fr/hal-01378443

[26] P. M. CONGEDO. Introduction to Polynomial Chaos methods, in "CNES Meeting", Toulouse, France, October2016, https://hal.inria.fr/hal-01378450

[27] P. M. CONGEDO. Intrusive methods for Uncertainty Quantification, in "Uncertainty quantification: theoryand application to algorithms, CFD and geosciences", Toulouse, France, May 2016, https://hal.inria.fr/hal-01378442

[28] P. M. CONGEDO. Numerical simulation and UQ in aerospace application, in "Inria@SiliconValley Work-shop", Paris, France, June 2016, https://hal.inria.fr/hal-01378440

[29] P. M. CONGEDO. Prédiction sous incertitudes d’écoulements hypersoniques autour de véhicules spatiauxpendant la rentrée atmosphérique, in "Journées Scientifiques Inria", Rennes, France, June 2016, https://hal.inria.fr/hal-01378444

[30] P. M. CONGEDO. Uncertainty Quantification in Computational Science : some examples of interactionbetween numerical simulation and experiments, in "Seminar at Laboratoire de Physique des Plasmas", Paris,France, September 2016, https://hal.inria.fr/hal-01378447



















[31] P. M. CONGEDO, A. CORTESI. A Kriging-PDD surrogate model for low-cost sensitivity analysis, in "AIAAConference", Washington, United States, June 2016, https://hal.inria.fr/hal-01378402

[32] P. M. CONGEDO, R. DACCORD, J. MELIS. Numerical and experimental characterization under uncertaintiesof a piston expander for exhaust heat recovery on heavy commercial vehicles, in "NICFD Conference",Varenna, Italy, October 2016, https://hal.inria.fr/hal-01378428

[33] P. M. CONGEDO, M. G. RODIO, R. ABGRALL. Numerical simulation of cavitating flows under uncertainty,in "NICFD Conference", Varenna, Italy, October 2016, https://hal.inria.fr/hal-01378423

[34] P. M. CONGEDO, M. G. RODIO. A robust equation of state for liquid-vapor mixture, in "ECCOMASConference", Crete, Greece, June 2016, https://hal.inria.fr/hal-01378406

[35] A. CORTESI, P. M. CONGEDO. A Kriging-PDD surrogate model for Uncertainty Quantification, in "ECCO-MAS Conference", Crete, Greece, June 2016, https://hal.inria.fr/hal-01378408

[36] A. CORTESI, P. M. CONGEDO. Rebuilding freestream atmospheric conditions using surface pressure and heatflux data, in "AIAA Conference", Washington, United States, June 2016, https://hal.inria.fr/hal-01378401

[37] F. FUSI, P. M. CONGEDO. An Adaptive Strategy on the Error of the Objective Functions for Uncertainty-Based Derivative-Free Optimization, in "SIAM UQ", Lausanne, Switzerland, April 2016, https://hal.inria.fr/hal-01378411

[38] G. MARTALO, C. BARANGER, J. MATHIAUD, P. M. CONGEDO, L. MIEUSSENS. Numerical computationand validation of extended boundary conditions for Navier-Stokes equations, in "30th International Sympo-sium on Rarefied Gas Dynamics", Victoria, Canada, July 2016, https://hal.inria.fr/hal-01378416

[39] V. MORAND, P. MERCIER, G. PRIGENT, E. BIGNON, P. M. CONGEDO. CNES activities on polynomialchaos expansion for uncertainty propagation, in "27th AAS/AIAA Space Flight Mechanics Meeting", SanAntonio, United States, May 2017, https://hal.inria.fr/hal-01378431

[40] L. NOUVEAU, H. BEAUGENDRE, C. DOBRZYNSKI, R. ABGRALL, M. RICCHIUTO. An adaptive, residualbased splitting approach for the time dependent penalized Navier Stokes equations, in "ECCOMAS Congress2016", Crete Island, Greece, June 2016, https://hal.inria.fr/hal-01403209

[41] N. RAZAALY, P. M. CONGEDO. Computation of low-probability events, in "UQ Meetings, Stanford Univer-sity", Stanford, United States, September 2016, https://hal.inria.fr/hal-01378449

[42] N. RAZAALY, P. M. CONGEDO. Computation of tail probabilities for non-classical gasdynamic phenomena,in "NICFD Conference", Varenna, Italy, October 2016, https://hal.inria.fr/hal-01378421

[43] F. SANSON, T. E. MAGIN, F. PANERAI, P. M. CONGEDO. Bayesian Reconstruction of Catalytic Propertiesof Thermal Protection Materials for Atmospheric Reentry, in "SIAM UQ", Lausanne, Switzerland, April 2016,https://hal.inria.fr/hal-01378409

[44] K. TANG, P. M. CONGEDO. Regression-Based Adaptive Sparse Polynomial Dimensional Decomposition forSensitivity Analysis in Fluids Simulation, in "SIAM UQ", Lausanne, Switzerland, April 2016, https://hal.inria.fr/hal-01378414


















[45] D. VIOLEAU, R. ATA, M. BENOIT, A. JOLY, S. ABADIE, L. CLOUS, M. MARTIN MEDINA, D. MORI-CHON, J. CHICHEPORTICHE, M. LE GAL, A. GAILLER, H. HEBERT, D. IMBERT, M. KAZOLEA, M.RICCHIUTO, S. LE ROY, R. PEDREROS, M. ROUSSEAU, K. PONS, R. MARCER, C. JOURNEAU, R. SILVAJACINTO. A database of validation cases for tsunami numerical modelling, in "4th IAHR Europe Congress -Sustainable hydraulics in the era of global change", Liege , Belgium, 2016, https://hal.inria.fr/hal-01390692

National Conferences with Proceedings

[46] L. NOUVEAU, H. BEAUGENDRE, C. DOBRZYNSKI, R. ABGRALL, M. RICCHIUTO. An ALE residualdistribution approach applied to the penalized Navier Stokes equations on adapted grids for moving solids, in"CANUM", Obernai, France, May 2016, https://hal.inria.fr/hal-01403192

Conferences without Proceedings

[47] S. BRULL, L. FORESTIER-COSTE, L. MIEUSSENS. Local velocity grids for deterministic simulations ofrarefied flows, in "30th International Symposium on Rarefied Gas Dynamics", VIctoria, Canada, July 2016,https://hal.archives-ouvertes.fr/hal-01397471

[48] A. MAZAHERI, V. PERRIER, M. RICCHIUTO. Hyperbolic Discontinuous Galerkin Scheme for Advection-Diffusion: Comparisons with BR2 & Symmetric IP Schemes, in "AIAA Aviation and Aeronautics Forum andExposition", Denver (CO), United States, June 2017, https://hal.inria.fr/hal-01390704

[49] A. MAZAHERI, M. RICCHIUTO, H. NISHIKAWA. Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian, in "46th AIAA Fluid Dynamics Conference, AIAAAviation and Aeronautics Forum and Exposition 2016", Washington D.C., United States, June 2016, https://hal.inria.fr/hal-01390685

Scientific Books (or Scientific Book chapters)

[50] P. M. CONGEDO, M. G. RODIO, R. ABGRALL. Investigation about uncertain metastable conditions incavitating flows, in "Uncertainty Quantification in Computational Science : Theory and Application in Fluidsand Structural Mechanics", October 2016, https://hal.inria.fr/hal-01378399

Research Reports

[51] L. ARPAIA, M. RICCHIUTO. r-adaptation for Shallow Water flows: conservation, well balancedness,efficiency, Inria Bordeaux Sud-Ouest, 2016, no RR-8956, https://hal.inria.fr/hal-01372496

[52] M. CLAEYS. Simulation using Abaqus of the vibration response of a structure to a turbulent boundary layernoise, Inria Bordeaux, équipe CARDAMOM, April 2016, no RT-0477, 23 p. , https://hal.inria.fr/hal-01299713

[53] M. KAZOLEA, A. I. DELIS. Irregular wave propagation with a 2DH Boussinesq-type model and anunstructured finite volume scheme, Inria Bordeaux Sud-Ouest, December 2016, no RR-9008, https://hal.inria.fr/hal-01419946

[54] M. KAZOLEA, A. FILIPPINI, M. RICCHIUTO, S. ABADIE, M. MARTIN MEDINA, D. MORICHON, C.JOURNEAU, R. MARCER, K. PONS, S. LE ROY, R. PEDREROS, M. ROUSSEAU. Wave propagation breaking,and overtoping on a 2D reef : a comparative evaluation of numerical codes for tsunami modelling , Inria,December 2016, no RR-9005, https://hal.inria.fr/hal-01414781














[55] M. KAZOLEA, M. RICCHIUTO. Wave breaking for Boussinesq-type models using a turbulence kinetic energymodel, Inria Bordeaux Sud-Ouest, March 2016, no RR-8781, https://hal.inria.fr/hal-01284629

[56] L. NOUVEAU, H. BEAUGENDRE, M. RICCHIUTO, C. DOBRZYNSKI, R. ABGRALL. An adaptive ALE resid-ual based penalization approach for laminar flows with moving bodies, Inria Bordeaux, équipe CARDAMOM,July 2016, no RR-8936, 15 p. , https://hal.inria.fr/hal-01348902

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[82] P. CONGEDO, J. WITTEVEEN, G. IACCARINO. A simplex-based numerical framework for simple and efficientrobust design optimization, in "Computational Optimization and Applications", 2013, vol. 56, pp. 231–251

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[91] C. ESKILSSON, J. PALM, A. P. ENGSIG-KARUP, U. BOSI, M. RICCHIUTO. Wave Induced Motions of Point-Absorbers: a Hierarchical Investigation of Hydrodynamic Models, in "11th European Wave and Tidal EnergyConference (EWTEC)", Nantes, France, September 2015, https://hal.archives-ouvertes.fr/hal-01168780

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